This is my .308 T/C Pro Hunter Contender. I have a new original Thompson Center 15" .30-06 barrel coming today from Haus Of Arms. I'm anxious to shoot it. I'm thinking of working up some cast bullet loads for it in the future. The latest edition, (6th Edition), of the new Sierra Bullets loading manual lists jacketed loads for the .30-06 in a 15" barrel up to 2,600 FPS with 150 grain bullets, and IMR 4064 powder.
The recoil is quite stout in .308, but controllable. Especially with no muzzle brake. I would imagine with the .30-06, it will be only slightly greater. Both the .308 and .30-06 are shot from plenty of rifles with 16" and 18" barrels. So shooting the same from a 15" barrel isn't that drastically different.