Are you talking about white-tail deer, mule deer, or what? Size does make a difference, but bullet placement is the most important aspect. I have been hunting white-tail deer in south Texas for 27 years--some are very nice size-- and have harvested at least one each season and two during most seasons. I have used a variety of calibers including 30-30 and .308 Winchester. My choice for the last 20 years has been .25-06 in 117 or 120 grain boat-tail bullets. I have never had a deer run more than 15 feet, but I am admittedly a meat eater--neck only--shooter. I am confident that most deer would succumb as quickly as a big white-tail given a properly placed shot. In my early days I longed for a .270 because I thought bigger and more powerful was better, but I have come to realize that shot placement is far and away the most important aspect of putting the deer on the ground. I choose boat-tail because of ballistic stability over distances. Most of my opportunities are at approximately 175 to 250 yards. Personally I think you waste money on fancy bullets like the Nosler Partition although I have nothing bad to say about them. I just think they are unnecessary. Mostly I choose Sierra brand--a medium price range, easily obtained bullet.
Moosie