The rabbit is much better for him than the cheeseburger, as many have already said. My mom used to feed her Yorkie mix Teddie everything she ate (cookies, chips, bacon, etc.) and Teddie got very fat and developed a back problem because she couldn't get around well. I sat down with my mom and explained to her that Teddie was going to die if she kept doing it, and she agreed to let me help. I started her out on an excellent low-fat kibble, which she denied at first (after eating all that junk), but after mixing some chicken broth in she ate it all. She is now at a healthy weight, she has gone from 25 pounds to 18...
She looks and acts so much healthier, and the vet said that probably saved her life...
The rabbit is just instinct...mine would kill and eat rats and rabbits if I let them. Someone just the other day was begging me to take care of their hamster for them for the weekend, and I just kept laughing. If I took care of a hamster, between 6 yorkies and 3 cats, that thing would not survive an hour lol.
I feed mine healthy things that I eat too...like carrots, fruit (except grapes of course), vegetables, yogurt, lean steak, grilled chicken, etc. I don't see any reason why they can't have those things. Like Michele said, I wouldn't feed them anything that's not healthy for ME either.