I have used a 39A for years, and shot maybe 10,000 rabbits with mine. Mine is a much older rifle, built in the 1960s and as smooth as the day it was made. I use a semi auto .22 magnum in my truck for pest control, but for hunting, and lets face it, most rounds are blasted off at cans, bits of wood and so on, you cant beat a lever action.
Always be extremly careful of a tube mag .22 as there is a slight risk of a round getting caught in the tube, and lathough you think it is unloaded it is not.
I have never shot a Henry, but handled one. They seem, to be quite honest, a bit light and cheap. Painted, not blued , plastic in some fittings. I dont like them, and they dont handle as well as the Marlin. I would look seriously at the Marlin.