I used to be the studio art director at iWin (casual game publisher/developer), so I’m quite familiar with casual game art and development.
I can’t think of any reason why you’d have to use vector to do this kind of style. I don’t see any reason why anyone with halfway decent drawing skills can’t paint everything you see in Angry Birds with just about any basic raster art program, using just the basic painting brushes. The main reason to use vector is for scalability, and in game art, you usually create the art assets at the highest resolution you’d need them (depending on what platforms the game will potentially be published on), and I have never come across any situation where using vectors was necessary in the production pipeline (except for maybe GUI-related assets).
But if you simply “enjoy” the process of using vector art programs over raster, then sure, you can try to replicate the Angry Birds look in a vector program. But you can just as easily do it with a raster art program. Angry Birds is not exactly high-end game art–any halfway decent artist should be able to do it.
If the Angry Bird artists did use vector art programs, then I suspect they like how easy it is to create the smooth curves needed for that style.
I personally don’t use vector art programs since I have no use for them for the stuff I do. But like I said, if you simply want to replicate the look, you can easily do it with raster-based art programs–you don’t have to do it with vector.
You might want to read these links:
http://gamedev.stackexchange.com/questions/30111/why-dont-more-games-use-vector-art
http://www.cocos2d-iphone.org/forum/topic/13511