I'm rather allergic to both but If push came to shove I'd go with cats.
It's rare that I find a cat I like but; its even more rare to find a dog I can stand.
Cats are rather solitary, they usually leave you alone. Some are playful at times, a bit annoying when they bring you their evening 'catch' and can even be a downright nuisance when they spray their 'territory' inside your house.
On the other hand there's dogs. Slobbery, messy, more maintenance , more destructive, some just won't leave you alone, plus they can be loud as hell.
To be fair, there's been a few select that I don't mind, and even a few I enjoy being around but generally, if its not a pet in my house then; its a good pet!