As posted above, YMMV.
I've owned a couple of both .358 Winchester's and .350 Rem Mag's, in Ruger 77's and BLR's, and have found that my preference lies with the .358 Win.
I find the .358 Win ammo more compact, easily made from .308 empty brass should the need arise (although can set up a dangerous situation, .358 slug /.308 headstamp), and isn't a belted case with that design's attendant needs like special shellholders, ammo carriers, primers, etc, etc, etc.
I especially would like what's currently unobtainium - a new, wood-stocked .358 Ruger Hawkeye w/iron sights as issue, or a .358 M77- RSI/ International.
BTW - Have you checked out the relatively new .338 Federal ?
It's a .358 Win clone, currently available in Ruger M-77's, and looks to be a very acceptable .358 substitute.
It may very well turn out to be the best of both worlds. Time will tell.