I'd have to go with cats (though I like both).
Reasons?
1. Cats don't usually run after people, yank of leashes (if they have any) and they can stay indoors.
2. You don't have to get up all the time to walk them around.
3. They have a fun way to play where disabled children can easily sit on the floor and roll a ball or wave a toy around.
4. Cats sense when you're sick (not that dogs don't) and will often curl up with you to keep you company.
5. Cats don't get that big and their food can stay much longer if you give them a certain amount a day.
Dogs often will want/get more.
6. Cats are independent. You can leave them at the house without being worried they'll get into too much mischief.
7. Cats can be declawed (though I think it's cruel) and most of them don't bite.
8. If a cat licks you, you most likely won't find your entire body slobbered on.
9. Some dogs drool and it gets messy.
10. Young children are often afraid of dogs, but find cats cute.
11. Often easy to train to use the litterbox.
I like dogs too, but I'm going with the cats.