Both those calibers are excellent choices for what you have in mind. I have hunted with both, and killed deer with both. What I feel is most notewothy is the fact that the .270 is pretty much done with bullet choices at 150 gr., and you have more options with the 7 mag if you wish to pursue it. The .270 seems to do best with bullets in the 130 gr, range, depending on twist, and the 7mag seems to shine with 140 rangeand higher bullets. You need to decide on what you wish to shoot bullet-wise for the game you wish to hunt, and make your choice accordingly.
I know that the devotees of each will chime in, but for my money, with deer-sized game at reasonable ranges, the .270 is a tough act to follow, and only a slight whisper away from the 7 mag in factory ammo