kicker
The '06 with heavy bullets (180 and up) and certain stocks and body styles can be a kicker. My sister (no kiddin) had a S&W 1500 that Dad bought her that they shot 180's out of, and the thing was a vicious kicker. Sis shot it well, she ain't no ordinary gal.
If you haven't checked, and the game your after does not require a heavy slug, try 150 gr slugs. Modern premo bullets have in many cases superceded the old heavy cup and core bullets. Too, I think Rem sells reduced recoil rounds for the '06, featuring lighter slugs and milder charges, as a factory load. Also, plus one to a fit assessment and a premo pad like the Kick-eeze.
If you just have to have a new rifle, one of the oft touted advantages to the .270 was that, w/ 130 gr slugs, it was more manageable. The 7mm-08 and the 7x57 are also full power ctgs with reps as mild shooters.