So my most recent run of playing Civilization starting December I mixed it up a bit playing games in IV, V, and VI, (going unmodded and with the final expansion of each) to try and see objectively how they stack up against each other. I generally played huge maps on normal or marathon on emperor difficulty. It will be a big post so I'm just going to do one game review at a time.
Civ IV
The last of the original style Civilization. I played this last in my run, it was hard going back to unit stacks and had to drop back from Emperor to Monarch difficulty. From a performance perspective being a 15 year old game it runs just amazing today, playing the highest map size and having maps generated and loaded in seconds and time between turns barely noticeable.
The positive of stacks is the AI handles them much better, the negative is it's much less compelling gameplay and every border is a disaster waiting to happen. Overall I loved all the different improvements, the diversity in yields, culture border expansion and city flipping, and the in game map editor. Also it's technically 'cheating' but for limited use having the ingame map editor always onhand was great. A subtle difference I liked was that early game scouting was more limited, as your scouts could beat roaming animals but when human barbarians come out they get killed, which keeps the map darker in the early game. Also thought the tech tree was much better, being more 'tall' than 'wide' giving you more options to choose from at any given time and more interaction between techs.
On the negative side, again harder to go back to stacks as they're much more annoying and less compelling gameplay wise. Unit combat being battledome where two enter one leaves and it's all up to the RNG can be frustrating, as you're going to lose key units when they have a 90% chance of success because over the course of a game those 10% chances will come up. Diplomacy is just horrible, with it being hard to get any positive modifier and the AI constantly making demands give me this or stop trading (even just open borders counts here) with them, where agreeing or disagreeing mostly overally just adds more negative modifiers. The civics and religion system was pretty good compared to Civ I-III, but overall much less compelling than V/V^ and meant you were almost always going to follow the same style as you progress. Similarly the old style 'each leader gets two traits from a list of 8' isn't nearly as compelling as Civ V/VI unique abilities and means the games feel more the same regardless of leader.
Final judgment: if you haven't played Civ and have an older machine/slower laptop still a very solid game, but while it's more complex in a number of ways the overall gameplay is a good bit more rigid or less compelling and you're probably better off with V or VI.