Yup, it's hotly contested.
The Civ2 crowd is really devoted; they've figured out ways to make a 16bit game work with 64bit Windows 7 and 8, for cryin' out loud. I liked the wonder movies, and the advisors, and the elastic nature of science and commerce. One could (I tried, and didn't really execute it well) get insane amounts of science and tech by building caravans and freight units, and delivering them to the proper cities. Units defending in a city were really, really hard to beat, IIRC.
The Civ3 group (here) love the streamlined graphics, cultural boundaries, unique units, and many gameplay improvments over Civ2. Certain Civ4 concepts seem overcomplex, and the Civ4 graphics have few fans here. The game also runs *fast* on modern computers; much much faster than Civ5.
The Civ4 fans feel that it is the logical conclusion and most evolved version of the Civ 1-2-3 generation. Spies are units again, and their missions make sense. Governments are not simple choices (republic/monarchy/democracy) but a set of interlocking civics, which can be / must be changed at different points in the game to best suit your situation. They feel strongly that several elements of Civ5 ruin their favorite parts of the game, and most shun Civ5.
Civ5 is a very different game; it is inspired by many of the Civ franchise ideas, but it is fundamentally different. The civics became social policies; once implemented, you can never un-implement them. Only one military unit may occupy a land hex, although they can stack with one civilian (e.g., worker or settler) unit. Cities can defend themselves, which I find cool. Land units can swim (embark on the water) without having to build boats and load them on/off boats. One can build a thriving, game-winning empire with only 4 cities. The Civ5 fans cannot understand the attraction of big stacks of units, or sprawling, 80-city empires.
Different strokes for different folks.