Actually, C3C > C4. Why? Here's a few reasons:
1) Expansion is simple and straightforward. No need to beeline for CoL 'cuz you're hemorrhaging gold with just a handful of cities. (True, ICS has been abused but it's possible to win at higher levels without resorting to it.)
2) As per Strong Reactions' comments above, the combat system is consistent and sensible.
a) Each unit has strengths and weaknesses reflected in their attack/defense values. No need to give grenadiers special advantages over riflemen (how come?), riflemen over mounted units, etc.
b) Mounted units can usually retreat from groundpounders (although apparently not so much with v1.22), which demonstrates their superior mobility. (Of course, they shouldn't have this advantage attacking cities, but hey, nothing's perfect, eh?)
c) Bombardment units are missile units. They do not engage in melee in real life, and they don't do it in C3C. Apparently, it's used in C4 to discourage SOD's. But wasn't there a better way?
d) City defenses are empirical, based on walls and settlement size. There are no "cultural defenses" that must be reduced before assaulting (like, were the Mongols baffled by Chinese arts and letters?).
e) Air bombardment can be lethal, as it should be. Some players think it makes bombers too powerful, but consider the impact real bombers--dive-, torpedo-, and level--had over land and sea during WWII, not to mention the present day.
f) Combat can spawn great military leaders. They can build powerful armies or inspire their subjects/citizens to heroic efforts at construction, features that echo what actually happened historically. Yet GML's are totally absent from vanilla C4, while the GML in Warlords just isn't the same (sorry, haven't played BTS or COL).
3)There are several practical ways of winning at higher difficulty on standard maps, especially domination, diplomatic, and space race. Unfortunately with C4 at, say, Noble or above, it's almost always space race, space race, or space race (I dunno about cultural, if you wanna play it).
4) Unit and combat animations are simple but neatly done (IMHO, anyway). They don't have the cartoonish looks and sounds of C4.
5) You can play warmonger during the modern age. With C4 you almost always have to knock it off around the end of industrial or face the risk of falling hopelessly behind tech-wise. In fact, it's hard to fight wars for long at any age for the same reason. At least in C3C you have the possibility of extorting techs from your victims (not nice, but the world just isn't fair!), even if nobody else trades with you.
6) Oh yeah, "...and no religion too."
Thanks for your kind attention, and don't let me stop you from playing your fave Civ version!