If we're talking about a "do-all" rifle, then based on 35 years of residence and hunting in Canada's Arctic I want a rifle which strongly leans to the heavy side, rather than the light. When situations get hairy at close range, I want the rifle adequate for THAT time and place, not the lighter rifle suited for "lighter game". I've been there, and at bad-breath range the bigger rifle is a Godsend. A BIG cartridge reliably kills smaller game. The reverse IS NOT TRUE under emergency conditions!
Just last year I fell into a good deal on a Savage left-handed 116 (stainless/synthetic) in .338 Winchester, and took it north with me for an elk/whitetail hunt on my brother's place in NW Alberta. My shot at a whitetail buck came in failing light at 295 laser-measured yards. The shot was a bang-flop affair, and the 225-grain TSX wasted NOTHING, not a single pound of meat, with a ribcage hit. There's not a lighter rifle in the entire world that could have done the job any better, and I was still perfectly prepared for the elk and grizzly common to the area.
You can't sensibly carry a rifle "adequate" for the easiest cases, and still expect it to carry the load when it's eyeball-to-eyeball with a large and nasty critter. Prepare for the WORST case, not the best.
I think the stainless Savage 116 in .375 (if available) would be just fine, assuming the use of good bullets. Otherwise, the .338 is also great with GOOD bullets. I'd likely cut the barrel to 20 or 21" for an all-round rifle, and this would have very little effect on velocities while making it handier in tight quarters.