You never mentioned what ranges you would be shooting but my choice between
Those 2 it would be the 06. More than enough out to 300 or so yards provided you understand ballistics.
My choice in caliber after 20+ years of trying everything is the .257 Weatherby
300 yards is the max i will even try to hit a deer and with the 257 i can hold dead on from 0-300. No ranging/thinking/clicking/bullet drop scope crap. Just aim and shoot. The only negatives to me would be dealing with the 26’’ barrel in a shooting house and the high cost of ammo. Just my 2 cents.