. And I would say that it IS stressful because you know that the AI is receiving enormous bonuses that allow it to build everything
It doesn't
quite build everything everywhere, it prioritizes what it needs. That's why it performs better than you even on Prince where its bonuses aren't many. It shouldn't be able to do so much better than you if you have some experience of playing the game.
Unlimited choice but nowhere near enough time to build everything ... at least until you are in the modern era with size 30 cities
But you're not supposed to build everything even in the late game, you're supposed to choose according to location, goals, priorities and needs for synergy etc. It's a strategy game. It would be a totally pointless game if it let you get the cash to simply get everything everywhere and as soon as available.
Someone already mentioned that if you're so strangled for cash you probably build more units than you actually would need if you honed your defense skills a bit - learn to use terrain to your advantage etc., and probably pay maintenance on early roads for nothing (the rule of thumb is to wait until the city you connect to your capital is at least equal in size to the # of tiles separating it from your capital (or other city), so it pays for the road maintenance and generate profit from the connection). I know some people used to pre-build roads for future cities so they're instantly connected when they are founded. In Civ 5 it's an absolute "don't".
You probably also build too many buildings or too early (and the wrong ones), and they drain your treasury with little or even no benefit at all (a Lighthouse is all well and good, but if you won't work those water tiles for 200 more turns, you shouldn't build one just because you've now got the tech to do it). It probably means you focus too much on getting your production tiles enhanced and worked not to miss your Wonders, which in turn slows your growth because you've delayed building farms, which means less pop, less gpt and above all, less science.
Wonder spamming is a bad addiction. A lot of time the turns are much better spent on getting the right buildings or units for your strategy.
In most situations avoid the GL if you're not working a strategy to get Philosophy from it and thus be able to start on the National College immediately (on Prince, it
is a good strategy almost certain to give you the tech lead early. Since the patch you need to keep going toward Education and keep growing or the AI might eventually catch up, though). If you've expanded early and won't be able to start the NC before your new 2 pop city finally builds a library in 40 turns, you've wasted the benefit and should have built something else and beeline Philosophy while you get your last libraries up instead (and yes, the NC is important enough you might want to delay expansion beyond 2-3 cities before you build it).
Don't build Terra Cotta Army if you've got a small army and no intent to go to war offensively. Don't build the Great Wall if you don't need the defense bonus. Don't build the Great Lighthouse if your coastal city won't need a Lighthouse for a hundred of turns; that +1 movement +1 sight isn't worth it, especially if you're not keen on relying on a navy later, and if you do build the Great Lighthouse, make sure to use that edge to get those fast caravels up early to explore and be the one to found the WC, to find NW and CS. The Hanging Gardens isn't that great if you can get cargo ships up in that time that will give your city +8 food...
There's no point to building Stonehenge if once you get a religion you do nothing or not much with it, or if it won't really serve your strategy. Spend those hammers on getting an edge on growth (not Stonehenge but a granary), science, culture or something else instead.
Etc.
Beating the AI to Wonders sure is fun, but going for too many while most aren't even useful to your stragegy is another reason why you struggle so much in your games and haven't got the useful buildings up when you should. While you do that, the AI builds what it can use, and it's how you end up losing or struggling too much. It also invites AI aggression. Sometime it's even good strategy to let the AI waste its best city to build a Wonder (especially since it often can't make much of its benefits... Petra built in cities with just 2-3 desert tiles and such).
Something to be more careful about than before even on Prince: grow and tech well. The AI used to handle badly the science buildings, now it's much better. You need to keep up. Some very wide civs have become more dangerous in the late game as a result. A wide Bismarck often sucked, unable to keep up in science with the tall civs. Now he's likely to gain a few techs on everyone after Industrial if you let him grow too big, because he will have those Universities, PS and RL up, and his NC... Same for Catherine and Casimir.
Another problem you might have is that you worry too much about the score board and getting in the first position and staying there through the game. Trying to get and stay in first position often lead to bad strategic decisions (too many Wonders, for one thing), and there are many advantages to remaining in the "middle pack" - in diplomacy and with lowering aggression notably.
Once you're solidly in the tech lead and have your tech buildings up, it can be the right time to get those Wonders. Again, those that help your actual strategy, or that block the AI's if they have an edge in something.
