The way I understand it is that NSInteger et al. are architecture safe versions of the corresponding C types. Basically their size vary depending on the architecture, but NSInteger, for example, is guaranteed to hold any valid pointer for the current architecture.
Apple recommends that you use these to work with OS X 10.5 and onwards, and Apple’s API:s will use them, so it’s definitely a good idea to get into the habit of using them. They require a little more typing, but apart from that it doesn’t seem to be any reason not to use them.