This is a very hard choice. I'd have to say that overall, Infinity Ward did a better job. As far as CoD 1,2, MW, and MW2, they are all great games (in their own ways.)
Offline Aspects:
I would say that Call of Duty 1 and 2 were two of the best. It's hard to make another WWII game without repeating itself, so I have to give a one up to IW on that one. Their stories were both great, and the gameplay was breathtaking on both of them. I believe they had high replay value.
Call of Duty 3 was just pure awful I thought. I beat it and all, and it was ok, but I don't believe there was any spark to the game. The story was somewhat bland, and even though you could interact with vehicles and all, it was still just another WWII game.
World at War had a tremendous campaign, and it's replay value was really high to go back and try to beat on veteran. It doesn't have one of those walk through campaigns on it that you can beat in one sitting. If you played it non stop all day you could, but you couldn't do this without dying a few times. Overall, great offline aspects!
Online Aspects:
I never had the enjoyment of playing COD 1, 2, or 3 online. I will have no review to them.
Modern Warfare was one of THE BEST online games I've played to this day. They did a great job making a dozen different game types for people to play that fit their style of playing. It was always extremely fun, and it had a great atmosphere.
World at Wars online wasn't all too great to me. It seemed like it was too "slow paced" for a Call of Duty game. It was fun to play for a while, but there was just something about it I didn't enjoy. I didn't like them bringing in tanks either, as I thought this brought unfair advantages to the game.
Modern Warfare 2 was a great online game... For a while. I still play it with my friends and all of that, but I wouldn't play by myself. The community on MW2 is awful, and it's nothing but a bunch of foul mouthed 10 year olds who haven't hit puberty yet. That's one thing that really turns me off of Modern Warfare 2. Their are also too many exploits to this game to give people and unfair advantage. You also can't get into a single game lobby without one jerk in their who trash talks and thinks he's all that. I also hate the non legit 10 prestigers who think they are so much better than you because they always use some kind of hack, mod, or glitch in the game. I think MW2 overall went somewhat backwards from MW1.
These are all my opinions, and I know that there are jerks on every game, I just feel that MW2 is the worst for this and for people who don't play fairly such as boosters and modders. Please realize that I know this is in other games also, just MW2 takes the cake again.
The best Call of Duty game in my opinion was Big Red One. I absolutely loved this game. I played through it 4 or 5 times on veteran difficulty, and I could go back and play it if my PS2 still worked. I just think it had the best story, character development, and you could get attached to the characters.
But there's my rant, tell me what you think!