I've shot deer with a 45/70, and have not had any of them complain.
You don't handload, and you're buying a new gun, so perhaps think about the 450 Marlin. Factory ammo is loaded toward the higher end of the cartridge's capabilities, as opposed to factory 45/70 ammo which can be on the lame side, except maybe Hornady Leverevolution and some of the othe small makers like Buffalo Bore and Garrett , which are not caheap by any means.
If you hit a deer forward of the diaphram with a 45 caliber bullet moving around 2000 fps, the deer will expire pretty quickly. This should be easy to do with either the 45/70 or 450 Marlin. Ballistically, Id say these guns are about on par with the higher end sabot slugs, so you may not see any real ballistic advantage to using a rifle. I'd say the advantage would lie in relative accuracy (perhaps) and handiness of the rifle.
I have an 1895 SS in 45/70 with a peepsight, that is awesome in the woods. I would much prefer to hunt with it than my Marlin 512 bolt action slug gun, though both are accurate enough for the areas I hunt.