I own both, a Winchester Model 70 in 7mm Rem Mag and a Stevens Model 200 in 300 Win Mag.
Both put any animal I have shot DRT 95% of the time, both have amazing accuracy and are flat shooting at ranges that a 30-30 could only dream of, and both beat the hell out of your shoulder.
I haven't reloaded for the 7mm Rem Mag yet due to the fact that I have enough factory ammo to last me another 3-4 years of hunting season. It's more of a safe-queen anyways since I bought my 300 Win Mag a few years ago...
As for the 300, I'm liking the 165 gr. GameKing loads I have made up to dispatch anything in the mountains of Virginia within 500 yards. Pushing a .308 dia 165 gr. pill at around 3,000 fps is very effective on critters. Not saying that a 140-150 gr. pill out of the 7mm Rem Mag traveling just a bit faster won't do it, I just like the extra mass to help push through both shoulders at 300 yards. This might change after I shoot up all of that $2 a shot 7mm Rem Mag stuff I've got and start loading for that....
Honestly though, no big difference. The 7mm's will have a slight edge on ballistics, especially after 500 yards over the .308 dia bullets. Both can pack a lot of powder behind the bullet too. Both are very effective and very versatile rounds.