I'd go with a 270Win. Yes, the 7mm-08 can be used with heavier bullets such as the
175gr., but these are not factory loaded. Factory loads only go up to about 150gr. for
the 7-08. Bullet diameters are nearly identical (270 = .277" vs. 7mm = .284"). The only advantage for a 7-08, if it means much to you, is that it's available in a short action
rifle. One thing for sure, the 270Win. has a lot more factory loadings available so unless you're into handloading the 270 would be the better way to go.
Fact is, when it comes to game killing power there isn't .02 worth of difference between the two for all practical purposes.
Find the rifle you like best, and then go for the cartridge. It'll probably end up being a
270Win. as it's also chambered in far more rifles.
Good luck.