I've owned both, and like both. Both will do a good job for you on larger game, especially with some of the higher performance loads like these:
.270 Win
Superformance 140gr SST - 3090fps
Superformance 130gr GMX - 3190fps
7mm RM
Superformance 139gr GMX - 3190fps
Superformance 162gr SST - 3030fps
Just choose the one you want more.
This is one comparison but there are many others.
Two Sierra screens on your monitor, or any two reloading books. One will always make the other a liar but it becomes your decision.
Much like the chicken - egg controversy, do you pick the bullet before the rifle or does the rifle come first?
When I bought my first rifle, a Model 700, the .30-06 was well reported on, and the 7 mm RM was relatively new by comparison. Already thinking of reloading, the bullet selection in .308 calibre was considerably better.
20 years later and with an elk tag in my pocket the search for a .338 WM started but there were none to be found but there was a 7mm RM. Comparisons of it versus the .30-06 left me with my original.
Comparing a 7 mm RM with a .270 must have equal comparisons. Barrel length, bullet weights, & ballistic coefficient. Sectional density might be another arguement but there is only 0.007 of an inch difference in the diametre of the two.
Rifle and fit and handling come first. Selecting the bullet is for further study.
I have a .280 Rem., and have had a .270 Win., a .30-06 (recently given to my son), and a .338. If this is the rifle of a lifetime that is one thing but when the "I think I need another rifle bug" strikes again the same advise will still be valid.
The .270 WSM was a valid additon to the comments . . . the "small ####" comment was not.