Rabbit is a good meat animal for home production. The meat, as jacyjones said, is low in fat, and requires a bit more care (basting, etc) to keep it from drying out when cooking.
I haven't butchered a rabbit or chicken for a couple of decades now, but when I did, I could do 4 or 5 rabbits in half the time it took me to do a chicken. (Granted I always made a complete mess of the poor bird and eventually decided the mess wasn't worth the trouble.)
Rabbits require a bit more care than chickens and since they are generally raised in separate hutches or cages, they do well with more human contact than a chicken seems to require. Startup costs will be higher for rabbits than for chickens, for housing them and also for acquiring breeding stock.
If you shop for breeders, be sure to visit the rabbitry before handing over any money. You will be looking for clean and alert bunnies, housed in clean conditions. You will generally know the minute you walk into the rabbitry if the bunnies are well cared for by the condition of their surroundings. If the place stinks and is filthy, don't even look at the poor bunnies as their surroundings will reflect the care they've received (or didn't receive.)
I'll be adding a small rabbitry to my mini-homestead soon, mainly because I miss having bunnies around. (I haven't eaten meat for around 10 years.) The poop is great for the garden and it is often used directly in the garden without composting, though there are many who will argue that no manure is safe to use without completely composting it first.
Wayne