I own a number of each and find they both work. For eastern deer hunting in the woods, where shots are rarely much over 100 yards, I like a short barreled .308. This year, I've drawn a Wyoming antelope tag, and my Tikka .270 is going along.
As far as accuracy goes, every .270 I've owned has shot well. Most of the .308s have shot well, but a couple were pretty fussy. In my experience, the .270 gets the nod for accuracy.
The .308 does the job with less powder. Typically 45 gr vs 60 gr. So I can load 4 .308 rounds for the same grain weight as 3 .270 rounds. Yes, I know they use different powders.
Both are a good choice.