I've been playing a lot of Civ 5 Gods & Kings lately. Here's how I'd compare 4 and 5.
Civ 5 has a more interesting opening game I think. You have more options: vertical development with Tradition, the usual REXing with Liberty, killing things with Honor, or you can mix & match. Depending on huts and barbarians you may get an early pantheon or an early city-state relationship which can change things. In Civ 4, you pretty much have to rush to connect strategic resources before the barbarians/ neighbors get to your gates, then either sack one of your neighbors (probably) or REX and put up a good wonder or two. Only after that do options open up for you.
Civ 5 has the worst closing game of any Civ I've played and it's been a perennial problem with the series. You get locked into chasing a particular victory condition early on if not instantly, and, since the game runs slower, there's a lot of clicking end turn towards the end of a game. Gods & Kings helps that a bit with the intrigue complicating formerly super-boring diplomatic victories and some other stuff, but it still gets to be a slog. Civ 4 BTS on the other hand has the most interesting endgame of any Civ except maybe Alpha Centauri - AIs can take stabs at you, or their own victories, that can actually surprise you.
Diplomacy in Civ 5 is crap and Gods & Kings only helps it some. Civ 4 diplomacy isn't the best, but at least it feels like diplomacy. "Declarations of Friendship"
Battles: Civ 5 unit-per-hex battles are interesting, if goofily unrealistic at the scale at which they are presented. At the Civ scale, doomstacks actually seem to make a bit more sense, at least until they get really absurd. But, more importantly, Civ 4 can handle doomstacks and Civ 5 can't handle hex combat. If I want to routinely destroy the AI at bad odds, that's what Total War games are for
Gods and Kings does make fighting better, though: at least you can't murder an AI's entire land army with triremes.
Civ 4 does a better job of feeling like a grand-scale game, somehow. Partially it's because you're moving around more units. Partially it's because you don't have quests from NPCs I mean city-states. Partially it's because Civ 4 has wonder movies and endgame movies and Civ 5 just has the stills.