I have a '92 Winchester in .45 Colt, and I'd not hesitate to use it for hunting deer. It's my saddle gun when I'm bear hunting and such, but it'd kill a deer easily enough.
Range would be similar to most muzzleloaders, with quicker follow up shots.
Shotguns are generally limited to two rounds in the chamber, and most aren't all that accurate (although they can be). Because of the weight of slugs and the pattern of shot, they don't work well for longer range shots.
I've never hunting in Indiana, so I don't know how far shots are generally taken. Even so, I think a pistol caliber rifle would work as well or better than the others.
Of course, given the chance I'd do as suggested above; just hunt with each in their respective seasons. If limited to one, then I'd go with the rifle chambered in a pistol cartridge.
Personally, I'd use a .44 mag, or .45 Colt loaded heavy. I use 300 gr bullets in mine, pushed to about 1700 fps in the rifle.
Daryl