One will kill big game just as dead as the other.
The 7MM Rem Mag seems to be the most powerful rifle that most hunters can shoot off a beach w/o flinching. I know it is for me. I've seen men far bigger hunters than me suffer recoil shock from the .300 Win Mag.
The reality is the .270 Win, .280 Rem, and .30-06 will kill big game just as dead as any magnum. All a hunter has to do is place a bullet where it needs to be. There ain't a North American big game animal that's long for the world sans its heart and/or lungs.
Were I given a do-over, I'd buy only one rifle: a Sako AV in .280 Rem and never look back.