ORIGINAL: Superpig
Since you are buying your first rifle I will assume that you aren't a handloader. I would buy the 270 because there are a plethora of factory loads available for this rifle. As stated by another you can handload 175 grainers for the 7MM-08 but the long bullets protrude so far in the 7MM-08 case you will only get abouth 2400 fps of velocity. For the 270 if you handload you can get a 160 gr. bullet for it. I don't know of any 175 gr. factory ammo for the 7MM-08 or of a factory 160 for the 270. There are many controlled expansion bullets available for the 270 ranging from 130-150 gr. and Red Deer are smaller than North American elk so I think you will be fine with a controlled expansion bullet in the 140 to 150 gr. range. Look to Winchester Supreme 140 gr Fail Safe, Federal Premium loads the Barnes X, Trophy Bonded, & Nosler Partition, & I believe Remington still loads the 140 Grain A-Frame in its lineup.
federal loads a 150 grain speer hot cor for the 7mm-08, Also according to my Speer #13 manual handloaded 7mm-08 with 175 grain bullets has a range of velocities from 2312 fps up to 2628 fps depending what powder you use, the higher velocity is with RL19. I know listed velocites arent entirely accurate especially when it comes to different rifles because there are just to many variables that could be different from speers test barrels and the environment ie tempature and humidity which play a big role in velocity. either way you cant say you will only get 2400 fps from a 175 grainer in a 7mm-08.