.308 Win. for me. Dad's got a Remington 788 chambered in that cartridge, and I own a Savage 10FP. I think it's about the most accurate of the .30-caliber cartridges, and in my book accuracy is at the top of the heap when you're talking about hunting ANY game. But since we're talking about medium-sized game, then bullet energy and penetration isn't going to be that big a consideration.
Second choice in my book would be a tie: 7mm Rem. magnum or .270 Win.
Second choice in my book would be a tie: 7mm Rem. magnum or .270 Win.