European civs might have a tougher time, mostly because it's so crowded there. The west side of things especially, the Dutch, Danish, and/or French may never even get to settle because they're so close to each other. Those three in particular have a bit of a rough time because they'll have to contend with England's inevitable naval might and the encroaching conquest wave of Germany. The Netherlands will barely get any space for Polders or hell, numerous luxuries in particular, Denmark will have to directly compete with Sweden who loves to get other civs on his side, and good luck getting ANY wonders as France with Egypt present.
Germany is more a problem for the AI than they are awesome for you. There's a dearth of barbs poised to spawn in Europe, so basically you'll end up actually having to produce your own stuff, meaning Landsknechts will be an actual utility for once. And really, you'll want to do conquest. Sure, Germany's immediate lands are okay-sized for Europe, but given you're right next to the ever-militaristic Denmark and the usually-hostile France, you'll need to get them first, especially because they actually have bonuses they can capitalize on, whereas you're really just left with a half-cost Pikeman for most of the game.
Conflict between Rome and Venice is an inevitability, and it's very likely Venice will end up on the losing side unless it gets a serious fleet of Great Galleasses. Gratefully there's a big block of CSs close by that will only really have Poland and Byzantium/the Ottomans to deal with, but that will only help you so much when the Ballistas and Legions come a-knocking.
Spain and Portugal will definitely end up in conflict, but Spain has a BIT more space, and with Portugal you're aiming to set up colonies anyways. Portugal is very likely to get Gibraltar early-game, so as Spain, unless you're super lucky or quick on the ball, you're not getting the 500 gold for that. Really, you're not getting the 500 gold for anything, as your best shot is practically the Grand Mesa. Regardless, Gibraltar is super attractive for them, and next on the list is Sinai, which you'll have to basically conquer Egypt to get, but if you can, it is super great.
Austria could either be a problem or a ruin. They're basically dead-center in Europe, and downright completely unprotected from the Germans. However, they have a nice block of CSs to marry off, only they compete with Venice for those very same ones. It ultimately depends on who gets who first. Rome is likely to storm Venice, but Germany is likely to storm Austria. If they survive though, they're likely to be big problems in the long run.
Poland is probably better off on the map, with a decent amount of room, though Russia will likely compete with you for control of the big hole that is Belarus's absence. Poland's generally powerful, so with that lack of competition at their throats, they're generally alright. Russia gets a LOAD of space, it's just unlikely to be good space, and Mongolia might decide they want it.
The Huns being a problem depends on where they start, which can be a bit of a wild card. Some maps seem to put them more by Mongolia, which means they're likely more to be a threat to them and Russia, others tend to put them closer to Eastern Europe, which means Poland and the Ottomans/Byzantium will have to contend with them.
Speaking of those, whoever is present (I think a few maps actually put the Ottomans a bit farther out, around Ankara more than Istanbul, so that Byzantium gets Constantinople, who, in which case, is fairly shafted) has a middling experience. They're poised to get Turkish lands, but now in BNW they're skirting conflict with Assyria, who as we all know is far from friendly early-game. Thankfully, both of them get decent naval power, though that's hindered by the mass of city-states to the south-east, Egypt to the south, and Greece to the west. Their best bet is likely surging between Carthage and Egypt for land, though that presents its own problems.
Greece varies. On one hand, you have a nice block of city-states very close-by that will provide a nice power base. On the other, it's really hard to GO anywhere with you basically right in the center of a bunch of likely hostile civs. Then there's the matter of Venice and Austria, who, depending on the terrain, will be apt to go and eat up all your allied city-states. The Italian peninsula is tight, and all its CSs may not even get a chance to spawn. The Vatican just doesn't happen, Florence and Genoa are usually juuuuuuust too close to the purples, so Milan is the only one there with any reliability, and Rome is likely going that-away. With that in mind, Venice will tend to go towards Ragusa (accuracy!), and continue pushing in that direction, right towards Greece's closest allies. Austria will head there more from the north, and they can easily get more than Venice, unless you ally the CSs up in advance. Thankfully you have some early-game military power, though Venice is in a location hard to assault, so you might want to bop Austria first.
Onto Africa, Morocco is usually in good shape. They get a good chunk of Africa all to themselves, and a lot of it is desert which they will generally excel in, especially the useless flat desert of the Sahara. Plus they're within good trading distance of a lot of Europe, namely Portugal, Spain, even Rome. When war starts sparking up, the Berber Cavalry makes a good defense force. Their biggest issue is Carthage, who's somewhat close by, and the Songhai, who are likely to build up a military force soon enough. Carthage isn't likely to claim desert lands though, so you can maybe get away with them. You have a good shot at Gibraltar, though it's not a super awesome wonder, but it can be nice, but Portugal and Spain are in the running for it.
The Songhai are also in decent shape. Barb camps will be plentiful in Africa and you can make a neat profit from them, and you've got passable land around you. Nobody to really directly compete with you. Morocco's the only super close one and they're rarely hostile, and you can make lots of money off trading with them too. They'll typically end up in pretty good shape mid-to-late game, as they have potential to just own the entire western coast of Africa with basically no resistance, though Portugal will likely try for there.
Carthage is in much the same boat as Morocco, though with more hostile civs close by. The coast land you can take up is scarce with the crowding of the Mediterranean. A good strategy could well to be just to cut south and build up your naval empire around the Congo and stuff, since basically nobody is there.
Egypt can be tough. You may outright not get a chance to build wonders, not with Assyria very close by, the Ottomans even nearer, Greece just to the north, Carthage to the west, and Ethiopia in the way down south. Make good use of those War Chariots early on, they're going to be a vital defense force. They do get Mt. Sinai, which means they'll likely be the big religious powerhouse in the Middle East, if not Europe.
Ethiopia is comfy. The Zulu is far, far away, their only real neighbor is Egypt (and Arabia if they get expansive), and you start off with easy access to ruins if they're on. Only real sticking point is that there's a bunch of silly city-states in the way to getting cities on the Indian Ocean, so if you want naval power, you'll need to jump on there. Eventually the Zulu will come, but then, you have nice defensive bonuses against them, so they really don't pose a threat. Kilimanjaro and Lake Victoria are nearby, capitalize on them.
The Zulu have a bit of a problem. They're basically the opposite of Europe - South Africa is totally deserted. This can be nice in some cases, but the Zulu are a war civ, and it's hard for them to get anywhere. They'll be lacking in science a lot because they have practically no civs to trade with, only city-states that sort of get in the way. You'll want to push north and start getting in contact with Arabia or so to trade with, but it can be a long way away, and ultimately a domination victory may just not be viable if you have all the civs present. I'd say try a bit of diplomatic play, there's more than a few CSs roundabouts with a decent variety of types. I THINK King Solomon's Mines will be placed around here, so you can make that city into a big production center.
The Middle East can get messy. Arabia has it easiest, they get, well, Arabia, and the usual bevy of trade options from that range. Assyria has lots of nice targets that will probably be raking in the science. Babylon has the biggest problem, namely, Assyria. You're apt to be getting lots of science, but then, that only makes you look tastier to those siege towers. You really want to make use of your defensive abilities against them. Persia is typically alright, not much to comment on them, very little is in their way.
Asia is odd. There's a lot of very hostile civs and a lot of very peaceful civs. India basically will only exist because of the Himalayas, otherwise the Mongols would run them over quick. They're likely to be the biggest religion powerhouse, with both Sri Pada and Kailash basically theirs for the picking, presuming you take out Colombo if it's there. Invest in Piety with them, they're definitely going to survive long, and can make a lot of early Faith.
Siam is tough. There's only four city-states even that close to you, and I think Malacca or Kuala Lumpur take each other's territory, so that makes three, since Hanoi's a given and Hong Kong's pretty close. You do have a shot with Lhasa, and Manila's not that far, and if you're fast enough, the Australian CSs are typically left untouched, but that still really makes a maximum of eight, MAYBE nine if you count Kyzyl, for you to get. And since the Mongols are likely to obliterate some, China will most likely decimate Hong Kong, and you have Indonesia breathing down your neck, you're unlikely to get far. You need defenses, and you MUST protect your city-states. It's also a good idea to really crank up the exploration so you can meet more CSs. Probably one of the more difficult ones in a TSL. You're sitting on strategically valuable land for China and the Mongols and are generally in Indonesia's way.
Korea is a bit like Siam, but possibly worse off. They're basically encircled by Japan, China, and possibly the Mongols. You're really not going to be able to meet ANY city-states to help you out. Gratefully, Korea is amazing at defense. The Hwacha means those encroaching forces are basically going to be toast, and the Turtle Ship could easily be used to conquer Japan outright. However, you do very much have to survive to make it to that point, which can be tough as Samurai, Chu-Ko-Nus and Keshiks could well be rolling by the time you get Hwachas. At least it's totally possible to prevail in the science game even without extensive trade routes.
Japan and China play a little bit similarly. Both are going to be doing heavy warmongering, though China is a bit more centrally located, and are going to be overall better at it, BUT they have the Mongols to deal with right from the get-go. Japan is a little bit safer, but doesn't have as much easy access. They're both solid, but they're both going to come into conflict with each other very quickly.
Mongols are self-explanatory. Crush everyone in your way. Don't even GO Honor, push Liberty so you can maintain the massive empire you intend to build. They will either be a nuisance or a superpower. Watch out for them.
Indonesia is a boss. You pretty much get all the SE Asian islands and Australia for free, with very little in the way. Krakatoa and Uluru are basically yours, no question. Their UA is a no-brainer to make use of. The Kris Swordsman is a super powerful UU in an era where most of your neighbors won't have their uniques yet, though Siam, maybe India if you get that far, do have UUs to hold the line. Since India is almost guaranteed to found a religion and Siam will almost certainly ally Lhasa super fast, the Candi can easily be getting buckets of Faith, even better if you actually have a religion of your own. They're one of the best civs on a TSL, and will definitely be a superpower later in the game. At least if Australia got into the game, there'd be competition for them ^^;
Crossing the oceans, Polynesia is...odd. By and far, I'll say they're the most open-ended civ on a TSL. They pretty much get the entire Pacific, though an AI Polynesia will rarely make good use of this. You basically have no imminent threats. Every last bit of civilization is incredibly far away, the closest thing you have to neighbors are Indonesia and the Shoshone, and the first city-states you'll end up meeting are like, Vancouver or Manila or Hanoi. You have total freedom...but. There's absolutely nothing in the Pacific. Some islands can be nice, yes, but there's no natural wonders or otherwise noteworthy terrain. So right from the beginning, you have to make a big choice. East or west? You're perfectly capable of making land claims in Australia and New Zealand, likely even faster than Indonesia since you can embark straight away. Or, you can opt to go to the Americas, where there's a significant chunk of land. Either way, you're not in the thick of things. If you choose to go east, then your biggest threat is essentially the Aztecs, and America once they get rolling. West, Indonesia's likely to get competitive. Really, there's not a set stage. Polynesia is what you make of it here.
Now, unto the Americas. In the north, you basically have three direct rivals, America, the Iroquois, and the Shoshone. America has so much to gain from wiping out the Shoshone. It's super good to conquer their vast stretches of land and buy up the remaining tiles for cheap, and blam, you have more territory than anyone in the world. But you're fighting a two-front war. The Iroquois are definitely going to be a competitor. America needs to bar them off, push them into crappier territory in Canada. The Iroquois needs to wipe America out, and fast. They can use the land better than America itself can. Lots of delicious forests means lots of money. The Shoshone needs to just plop cities everywhere, and defending it will come. Plenty of room for Pathfinders to dig up ruins, plus you've got three (lackluster) NWs ripe for the picking, so...pick that pantheon! These three have direct access to something that's at a premium in a TSL: land. There is extremely little in the way on the continent. But there's definitely competition. AI typically end up dividing it in thirds, with the Shoshone owning most of the western half, the Iroquois a lot of eastern Canada and some of the Midwest, and America all the rest, with some conquered between them. The only other factor at play are the Aztecs, and they're likely to come and try to play Mongols with you, and it's a good chance they'll own Texas, so push them out.
Speaking of the Aztecs, you're lucky as them. You're right next to a vast swath of open land where lots of enemy units will be rolling. Be the barbarians. Harass your northern neighbors, and conquer the inevitably wonder-spamming Mayans. Simple.
The Mayans are a bit...hm, I don't know what to think. They're kind of in trouble, being in a vice between the Aztecs and Incans, who tend to adore unit spam. I say as the Mayans, be the trading empire. Treat the Caribbean like it's the Mediterranean, as there's likely to be lots of nice coastal cities from America and the Aztecs. Hold the line and do culture victory-esque stuff, they're good at those.
The Inca can be trouble. They start in a place well suited to their UA, and what's worse, they pretty much get Potosi (and I think El Dorado too on some maps). They will have no lack of gold, and this combined with their tendency to mass unit spam means they might go on a serious conquering spree. So take caution when against them, and take advantage when playing as them.
And last but not least, Brazil. There is little I need to say as them. Pick the Culture from Jungles wonder, blaze your way to Brazilwood camps, control your Happiness to save Golden Ages for late in the game, and just be the tourism titan. They're well defended by all that Jungle, and nobody's nearby, aside from the Inca. Against them, I'd advise taking them out, they could easily suddenly sneak their way into a win, but more often than not they'll be ineffectual.
...this probably turned out too long. TSL maps do tend to bring out civs' unique facets very well, a lot of them are in positions where taking advantage of their uniques is not only advised, but practically necessary. Soooo yeah, /rant