You can always wussy load an '06
but you can't make a 25-06 into something that's reliable for the great bears. It would take very careful, close range shooting to make it a decent choice for black bear, elk or moose, too. If your 06 is a BAR commercial Browning auto, it will have rapidfire potential that no bolt action offers. For stopping fleeing cripples, for dog packs, for stopping charges, for use vs men. Loads like the O6 require a nice recoil pad, tho. Also, even while hunting, wear ear protection. Norton sonic "earvalves" work just fine.
The BAR is offered with an alloy receiver, making it a lb ligher for long hunts. Or stick with the steel one, for lessened recoil and greater durability. If you shoot a lot and carry it very little, the steel one makes more sense. and vice versa.
I prefer the Remington autos myself, but I always buy used guns, and testfire them before buying, or get a "right of refund" agreement, in writing.
3006 and even weaker loads have taken many hundreds of elephant. Poachers these days take them with AK's. They sneak up within 10 yds, fire a full auto burst or 2 into one lung, wait overnight, and look for the circling buzzards. The lung is 2ft in diameter. The tusker coughs up blood, inhales it into the other lung, and drowns. The 06, with Barnes "solids' to the brain, will drop one like a rock.
You can use 125 gr sp's for varmints, even 110 gr hp's. The 06 has done quite well in 1000 yd matches, better than the 308, actually, due to less drop and drift, with heavier bullets in the same diameter. It's got plenty of power for use on elk or moose to any humane firing distance, ie, 1/4 mile. It can get 180 gr btsp's to more velocity than the 308 can get with 165 gr bthp's.