Most cat studies show that small mammals, mainly rodents, rabbits or hares are the dominant prey of domestic cats. That conclusion comes from a study conducted in 1988 by BM Fitzgerald called “The diet of domestic cats and the impact on prey populations as published in The domestic cat: The biology of its behaviour. I must say that you cannot state that rabbits (or hares) are a main part of free-roaming domestic cats. It must be very rare indeed for a domestic cat to kill a rabbit but it does happen because adult rabbits are occasionally taken “but they appear to be near the upper limit of prey size; thus predation on lagomorphs is heavier on young of the species.”
The quote comes from the book Wild Cats of the World at page 105. What they are saying is that young rabbits are occasionally taken by domestic cats if they have the opportunity. But the opportunity won’t arise that often. That, I think, answers the question in the title. On an associated topic, adult Norway rats are also sometimes killed by cats but few domestic cats will attack aggressive adult Norway rats.
And this is an opportunity to restate the fact that “despite frequent accusations, birds do not figure prominently in cat diets except on islands” (source: same book). Ornithologists constantly complain about predation by domestic and feral cats on birds but they are harder to catch than land mammals such as mice and reptiles (in Australia for example) and therefore they are not at the top of the domestic cat menu.
SOME MORE ON PREDATION OF BIRDS: