I mean, each to their own and all that, but if pushed I would probably keep my HMR over my .22 - more reach, more accurate, more energy, less bouncy. Any legit rimfire quarry much beyond 100 yards, I'd just get closer or use the .222 anyway. And apart from nervy corvids, the first option is usually always the more sensible (certainly for things you might eat).
That being said, I rarely see a rabbit these days. If things were as they were a couple of decades ago, I'd probably rage at the price of HMR ammunition and speak up more for the humble .22lr with mod and subs! I do hope the bunnies bounce back one day soon (pun half intended).