I know a lot of people hate brakes but the less recoil a rifle has the better a person shoots. The simple fact is that brakes work. My oldest kiddo when she did not yet weigh 100 pounds was shooting full power .308 hunting loads, (155 Lapua Scenar) the same loads I use, in her rifle that was equipped with a brake. I simply had her double up on the ear pro during practice.
She would wear both plugs and muffs at practice, the slip in ear plugs when it was time to shoot deer and elk. After shooting multiple animals I asked her about stepping up from the 6mm Remington she used on her first deer to the .308 with a muzzle brake, and she said she could not tell the difference. She was very tall and scrawny and the recoil did not bother her in the least.
She popped this doe at a couple hundred yards never paid the recoil any notice at all.
Her and her grandpa:
They are simply effective.
This was her 2nd elk, and I think she may have been 110 at tops.
Both of the above animals were shot with the .308 155 Scenar loads, btw.
.308s are very effective on elk, and I recommend them frequently to people. A lot of times I recommend the 308 over the 30-06 simply due to ammo. The majority of 30-06 factory ammo is under-loaded, due to all the old 30-06 rifles out there, some of which are over 100 years old. I have had .308 and 30-06 factory ammo of the same projectile weight, in rifles of same barrel length and had the .308 have a higher velocity.
However some of the newer ammo, like Hornady's ELD line is at least putting out some decent numbers and that is why I suggested that load and the link above. I really consider the 30-06 a handloader's cartridge if you expect it to perform to its highest potential, but at least now lately Hornady is putting out some ammo that is reasonable in performance and price.
The Tikka .308 is really an amazing platform, but it takes a knowledgeable handloader to take full advantage of its potential. Due to the T3s being all built on the same action, you can shoot your regular all around155 Scenar hunting load and then switch to 220 Nosler Partitions, long loaded, or Hornady 212 ELD-Ms long loaded, with just a couple of easy mods to the rifle. But again, that is not a factory turn-key solution.