I'd take the .30-06 over the .270. Not only can you shoot a heavier bullet - which is better from a physics perspective, but the heavier bullets are constructed more solidly - less expansion and better penetration, particularly if you hit a big shoulder bone.
The only place a .270 holds an edge over the .06 is that it is flatter shooting, so for long range shots (300+ yards), range estimation needs to be a bit less accurate. This is why Jack O'Conner championed it, and without Jack, the .270 wouldn't have near the popularity that it has today.