There's nothing wrong with the .270 Win. for elk hunting. My wife's great grandfather is 94 years old, still hunts elk every year, and has killed more elk than most people have ever seen. The only caliber he's ever used is the 270. That said I really like the .308 Winchester. I bought my wife one and it's a good all around cartridge, with ballistics not too far behind the tried and true 30-06. The other advantage is you can get relatively cheap ammo for the .308 so you can get a lot of practice time in without breaking the bank. If you do want to go with a bigger round and you're worried about recoil get yourself a Caldwell Lead Sled and use it when you're shooting from the bench. When you're shooting in the field you won't feel the recoil because you'll be too caught up in the moment.
AK Jeff