I was making the same decision just a few months ago. I was going back and forth going over all the posts I could find, looking at the ballistics, yada yada, and at the end of the day it came down to something real simple…factory ammo availability. I'm not a reloader so this was really important to me.
A quick look over at Midway this morning and there are 11 options available for 6.5 and over 50 for 308. When I looked at it a couple months ago when I made my mind up there was no 6.5 ammo available and still about 50 options for 308. I know there are other places to get ammo but to me it just really drove a point home that I'd rather have the cartridge that's more available because the differences otherwise for the application you're talking about are negligible in my opinion.