I've killed a bunch with both. I toted a A-bolt II in 7-08 from about 2002 till 2010, then went to a .308 Model 75 Finnlight, been toting it for 14 years . They are both fine whitetail rounds , and both worked great for me. I'll throw out some info.
308 is a great round , inherently accurate , wide range of bullets weights and easy to find ammo. I like 150-165 ish grain bullets. Great woods caliber .
7-08 is also great . has less choices for bullet weights than 308 , ammo not as easy to find. I like 140ish in 7-08. Little better long range than the 308. Perhaps a tad lighter recoil .
You can't go wrong with either , if you have shots longer than 300 yards I'd lean towards the 7-08, otherwise , flip a coin .



"Why do you ask"?

Too many people spend money they don't have , on things they don't need, to impress people they don't know.