I am by no means an expert on these rifles but I do own an M1A and know a little about the M1. They are both great-shooting rifles and very accurate. They are both heavy and wouldn't be my choice of rifle to lug around while hunting big game. The M1 shoots 30-06 and the M1A shoots 7.62x51/.308, both great cartridges for big game. The M14 action is basically an upgraded version of the M1, with a 20-round detachable magazine instead of the 8-round internal clip mechanism. There are other differences also. The only reason I said neither rifle would be my first choice for hunting is because I prefer a lighter bolt-action rifle with optics. I think both the M1 and M14 are fantastic battle rifles and a lot of fun to shoot.
For the purpose of deer, I think it would be 6 of 1, half dozen of the other! With the exception of the caliber. 308 (7.62 NATO) in the M-14 military/M1A1 Springfield Armory, would be adequate for deer, 30-06 in the M1 Garand (if that is what you meant), would be just a little more than the 308 and I think most would rate the 30-06 as more than adequate for deer.
Either one would serve fine for deer hunting. I believe there is a low cap mag for the M1A/M14. And I think it might be easier to scope the M1A/M14. I agree, 6 of one, half a dozen the other. This may just have to come down to personal preference.
I think .308 is cheaper too, but I haven't checked the prices lately, as I don't have either a .30-06 or .308.
~snip~ I believe there is a low cap mag for the M1A/M14. ~snip~
......makes me think, might be a good idea to check your intended hunting area laws. The M1 Garand is an 8 shot magazine and might not be approved if your area restricts magazine count down to 5 rounds! Although most states I'm familiar with are 10 round magazines.