I'll take a stab at that, I guess.
So... we can mostly agree that Call of Duty 4: Modern Warfare was pretty decent, right? It brought the mainstream FPS genre out of the 1940's, had pretty solid gameplay even by today's standards, and had a story that was sort of like a Tom Clancy novel as directed by James Cameron with a Harry Gregson-Williams soundtrack to boot. With each game that's come out since then in the series, it seems like they (Infinity Ward in particular, but Treyarch is certainly guilty of it too) have been treading further and further away from the Tom Clancy roots and straying closer and closer to Michael Bay territory. With each new game the goal seems to be setting up the story to do nothing more than provide bigger set pieces than the last. The result is a shorter game that boils down to nothing more than a chain of set pieces loosely strung together by giant fiery explosions, the corpses of dead player characters, and a huge amount of thinly veiled xenophobia.
So I guess that's my answer. Each game ups the stakes over the last one, and that's more or less what differentiates them. You want to see bigger and more ridiculously outlandish set pieces in your Call of Duty game, you get whichever one has the biggest number at the end until you reach the point where you're suspending so much disbelief that you actually begin to feel physical pain (from all the facepalming, most likely). Story and gameplay only really exist to introduce various types of brown-skinned or Russian stereotypes (that you'll likely gun down without remorse) and string you along to the next big fiery explosion fest.
But who really plays CoD for the story, right? It's all about the MULTIPLAYER, man! In that case, you're paying $60 each year for new set of maps and some new weapon skins for weapons that are functionally more or less the same as the previous game anyway (see: MW2 FAMAS vs. MW3 Type-95).
And note that I actually like the CoD games. Sometimes I need to just come home from work, turn off my brain for a while, and smile like an idiot at all the pretty explosions.
