It is possible to feed rabbits---babies---to BPs. I'm not sure if it's more nutritional or not, but I know of people that do.
Everything said earlier is true. It's going to cost a lot to raise rabbits. But, if you would prefer to raise rabbits to rats (which I can understand) you should go for it. Just understand that you will be spending more money initially getting things going---maybe more than you'll be saving in the long run.