I never played multiplayer, not in 2 nor in 4. Mind you, I'm playing the 360 version, and I played 2 at the Mac.
First off, the biggest difference is obviously WWII vs now. I like the missions better, and their story as well. Whereas in CoD 2 you were killing Germans generally, in CoD 4 you fight terrorist groups and the like. When you're the American bloke, you fight in an urban setting in the ME; when you're the British bloke you generally kill Russian ultranationalists that are supplying the other bad guys. There's one mission in particular that I loved, which I can say takes place in Chernobyl without giving away too much. I felt much more immersed in this game than the prequel.
I'm hard pressed to explain the differences though, it's been a long time since I've played CoD 2. But I liked CoD 4 much better.