The 308 can be a handfull, I don't think It would go well, with the reduced eye relief. I have shot them on 223 and 22 Hornet
Mark
I actually have a striker in 308 with a factory muzzle break. My 5'6" wife loves to shoot this gun, but I would be willing to bet that if it didn't have a break she wouldn't be shooting it. The gun does carry a little recoil with the break turned off.
I do have a 2-7 Burris pistol scope on top of this gun and to be honest that is plenty of scope for what I use this gun for. I don't know what your application is, but it's something to consider..