I have a .30-06 and harvested a lot of meat with it.
I also have a Weatherby in 300 wthby mag. It's still new. Never fired. Never even had a scope mounted on it. Just sits in the safe. Why ? Because someone convinced me that it was much better than a .30-06.
Ammo- $80.00 a box
Recoil- Substantially more.
Noise- Overly Excessive... and I don't need to further damage my hearing (Thanks Three Dog Night and Ted Nugent).
As for larger game, ie: bears, moose etc. If you're going to a larger caliber, go to a .338 or .375 of some flavor. I currently have a .338 win mag. It seems to me that my .338 WM has more recoil than the trusty old .375 H&H. And if you ever decide to go to Africa for dangerous game, you'll already have a .375 H&H. Just mu humble opinion.
Last, but not least... SHOT PLACEMENT... SHOT PLACEMENT... SHOT PLACEMENT
A well placed and ethical shot is far better that a poor shot with a heavy magnum. So, as others have stated, if you're recoil sensitive, shoot the .270 or .30-06.
Jeff