@ehBeth,
I don't believe in locking up animals. If you are going to have a pet, then it should be exactly that, a pet. Having too many pets, means the favourite or most well trained is going to get the most attention, then the rest miss out.
I trained my cat to "sit".. Still working on training him to stop friggen stealing any food he can get his hands on, even though he's fed well and wormed.
Do you worm your cats, ensure they don't have fleas?
Anyways. A rabbit can be trained as well, to use a kitty litter tray and live only caged at night, to sleep if you have an enclosed area, but they too need, worming, flea treatments and (not from the supermarket), from a vet. They can pretty well be close to what a cat is like, minus the load meows when they want something but it takes time to build a bond and trust with a Rabbit, mine lets me put him on his back and tickle his belly and he thumps in the morning suggesting I race over and let him out his 2 storey cage and he throws toilet rolls around when he is "suggesting" he wants to play, and then he eats some of my plants grrrr, so I try to get parsley, spinach, or a couple grapes over to him so he gets full and leaves them well alone.
I've had birds too, off course I hate them being caged. It's a pain, even with timber flooring to let them fly around... But, they too love mirrors, doing tricks and are smart, they will pretend they can't fly and so you take them outside to half fly around and play and they nick off, sheez...
I think animals need love and alot of attention, too many and all you are doing is going aweee that's cute, I want another pet...
I'd say neither unless you can spend alot of time with all of them, yet we can't do that, if in school or working.. One or two we can.