Never really cared much about the characters in WaW. In Cod4(in particularly the SAS missions) you were in a small group, who stayed close together. They seemed to say more too, talking about tactics, where to go, how you would proceed etc, which seemed to be less noticeable in all but a very few levels in WaW. It was more noticeable in MW2 than WaW, though the over the top plot didn't help. The thing that made me enjoy cod4 was that while you did end up saving the world I suppose, the whole game didn't feel like a quest to save the world. Most of the missions until quite late in the game were on a smaller scale, which made them a lot more interesting.
In WaW, some of my indifference towards the characters is probably caused by the AI. I remember for example, a trench lined by men on my team, up which several german soldiesr would consistently be allowed to run, ignored, and likeise ignoring all the men who they ran past to attack me...