Yes, as you know, I used to play Civ III intensively, and I 'd love to link back my experiences with Civ 5 to Civ III. When making a judgement about a game, it's almost inevitable that there's some sort of comparison with other games going on.
For me that other game would be Civ III. For most others here on the forums that other game would be Civ IV. That makes it difficult for me to post any view on Civ 5 here. When for example I say something positive about Civ 5 (I've many times defended Civ 5 here on the forums) someone here will respond 'Yes, but Civ IV had that as well,' and because I haven't played Civ IV it's then difficult for me to respond.
Speaking to a Civ III player like yourself would be easier for me, I think.
If I would have to make a short comparison between Civ III and Civ 5 I'd say that Civ 5 has gained a lot in combat, but lost in diplomacy and trade.
Combat has received a lot of attention from the developers. Compared to Civ III there's a lot more diversity between units and there's more depth in the promotion system. The one unit per tile restriction and also the way zone of control works makes combat a lot more tactical. More difficult for the AI to handle as well, but as a human player I feel I have to think much more when I'm attacking or defending than in Civ III. I find it a lot more satisfying than in Civ III, which was more about might by numbers and a disbalance between the AI and the human player when it came to armies and artillery.
There are some issues with one unit per tile, but you can see that the developers have spent a lot of time on combat and for me that has paid off.
What I find a strong point of Civ 5 as well is a more individual civ design. Each civ has a unique trait and either 2 unique units or 1 unique unit and a unique building or tile improvement.
I think again the difference is that the designers have made more of an effort, more than they did in Civ III in this area.
But in areas of diplomacy and trade I believe you can see that this effort has not been made. Especially trade is very simple. Regardless of personal preference, Civ 5 is simply lacking a lot of features that Civ III had; things have been taken out and not been replaced with something else.
Reputation for example. In Civ 5 you can sell all your resources to a civ and then attack them, there's no penalty. You don't do it, of course, it's cheating, but why does Civ 5 not have a system to protect the integrity of agreements? To me that's a basic element of game design, regardless what type of game it is.
The declaration of war itself does give a diplo penalty, which is good, but that penalty lasts for the rest of the game and counts for all civs, regardless of their relationship with the attacked party. If I declare on civ B because civ A asked me to do this, I even get a penalty with civ A.
There are lots of examples to give that to me point to a lack of attention from the developers. If I put a city close to civ A, civ A may dial me up and complain that I'm settling too close to them. Fine, but if civ A puts a city close to me, civ A may also dial me up and complain that I'm settling too close to them...
Civ 5 diplomacy has many cases where the idea was okay, but not enough tailoring has been done to make it fit.
It does affect the game experience when Japan calls me up one day to say they hate me, then call again right the day after to offer me their friendship. With not much else happening on the map the behaviour of such a civ then seems the result of some random dice rolls rather than a weighted calculation of actual interests. Too many looney messages and stances of civs spoil the idea that you're dealing with actual civs.
Most of the diplomacy howlers are quite patchable though, by just writing a bit more code. I think it's only suffering from a lack of attention. The problems are not a result of design choices, but a weak execution.
For the trade system it's different. Civ 5 has a very basic trade system, but it's clearly meant like that. There are no trade routes required, things have a fixed value, there are very few other dependencies as well. There's no tech trading.
The system isn't full of errors, like diplomacy, but just very basic. I'm not sure you would like this system, Spoonwood.
If you liked all the intricities that Civ III's trading system offered, with trade routes, reputation, population affecting the price of luxes, the value of techs depending on how many civs knew them, etc. etc. etc., then you're bound to miss some of that in Civ 5.
This is what I meant with that earlier post of mine. The people that criticized me were right, though, it's not for me to say what other will like or not like. There's a fair bunch of people that play Civ III as an always war game, which proves me wrong. For me playing civ III as an always war game means taking out its best parts - diplomacy and trade - and concentrating on its worst part - combat. But so many people play it like that, they must be getting their kicks from something I'm missing, let that be so.
But there are some generic features where civ 5 is lacking a bit and that are probably less dependent of taste. No adjustable AI aggression setting, no ability to turn movement animation off, no remembering of game setup preferences, no seednumbers... These things are no big deal for me, but it does illustrate there's not always a forward development. Sometimes steps back are being made.
Civ 5 is by no means a bad game, but as others have said, it could have been better.
No, I haven't played Civ V, or even Civ IV for that matter, and to speak honestly I have plenty 
