For 99% of hunting situations with factory ammo IMO there is really ZERO difference between the two. I mainly shoot a 7rem with 160gr Federal Trophy Bonded...compare that to the same projectile but 180gr 300win (I also have and shoot)....& the 7 rem is slightly better in the wind, only a couple inches difference in drop at 500yds, velocity is within 20fps or so @ 500, energy is about 200ftlbs lower in the 7 mag but still over 1500 @ 500.
I have both of these calibers in the exact same platform down to scope, rings, bipod, and sling. Real world shooting I don't even note a difference in recoil. Not saying one doesn't recoil more than the other but it is in no way for me noticeable.
With all that said you are gaining nothing by switching to a 7rem.