OK, I'll put my .02 in here.
I hunt deer with a 308 exclusively (not a Tikka only because I had not shot one before I bought this rifle). I usually shoot factory Hornady 150 SST rounds. Killed many a deer at 300+ yds (standing) and they dropped in their tracks for the most part. Longest tracking was 50 yds (high shoulder shots only).
I do have a Tikka T3 in 223 Rem. Love it! Shoot coyotes with it. Have been using Black Hills 52gr in it but am starting to use my reloads (new to reloading). I consistently get .5MOA with this rifle. Have no reason to believe that the 308 would be different.
The 308 IMHO is the perfect deer rifle. I have seen many deer not found by guys shooting 300 mags, 7mm mags, etc. The final line is shot placement. The 308 has minimal recoil, is relative cheap to shoot (compared to the 300 mag or 7mm mag) and, out to 350 yds is very accurate.
Actually, all my rifles shoot better than I can in a hunting environment.