Can't hunt with the 45-70? News to me. ;-)
I would pick the 45-70, as I handload and can run the lever quite a bit faster than I can a bolt.
Hard to argue with a 405 gr. flatnose pushing 2000 fps., but the .375 has a lot of killing power also. Probably a toss up.
I don't care for having a cocked bolt action on safe, and the lever carries nicely.