My answer:
Definitely more of a cat person than dog person, but at this point I'm pretty severely allergic to both, and probably mammals in general (I did have a mild reaction to a friend's horses and donkeys). I've noticed that I don't have as much trouble with indoor-outdoor cats than indoor-only animals though.
The only pets I've ever had in practice have been freshwater fish. Although, now that I finally live somewhere cool enough for it, I might get a chinchilla at some point. I've always liked those.