I have both and use both, both in Winchester M70 rifles. I like both. If I could only choose one, it'd be the .270 for sentimental reasons, plus it doesn't have that d@#n belt on the case. You can load up with a 150 gr partition and have a good load for heavier game. My .270 is heavier than my 7mm Mag, but both shoot very well - usually under 1 MOA, and often enough to not be a fluke under 1/2 MOA. Recoil is about the same, it seems to me. Off hand I don't notice, and on the bench, I always use a sandbag. I use the 7mm with 160 gr Partitions for Elk. As mentioned, you can go with heavier bullets in the 7mm - up to 175 gr.
Your choice, either one will do the job for you.