You will be very well served with either.
I love my 270WSM launching 140Accubonds.
In fact it started my love affair with the WSM case, & I now have a semi custom being built in 300WSM for a bit more range on bigger critters.
The 270WSM is very versatile, & has plenty of power, & shoots flat as a laserbeam. I've killed multiple Deer, & multiple Bears with mine, & my cousin has stacked up quite a few Deer, & Elk with his. ALL with handloaded 140 Accubonds over RL-19, shoving 3100fps.
Plus, there have been a lot of new, high B.C. bullets introduced lately that really make it shine, but depending on elevation, require a faster twist than factory offerings, to take advantage of.
As OrrHunter1 points out, the 300WSM is obviously going to offer the widest selection of bullets, from 55 grain accellerators to 230 grain Target bullets, & is also sufficient to smoke anything in North America if the opportunity ever arises. Maybe a once in a lifetime Alaska Moose hunt, or Colorado Elk hunt. Who knows. The 270WSM would also work just fine for this.
Recoil is a complete non issue. If you don't care for the recoil of a 300WSM, the 270WSM is not going to be enough less to hardly be noticeable. Plus the muzle brakes offered today take all the bite out of most any cartrige offered. Heck I've watched video of 12 year old girls, that Might weigh 90 lbs max, shooting deer past 600 yds from a 408 Cheytac based wildcat, thanks to a good muzle brake, & heavy barrel.
Recoil comparisons of WSM to WSM cases, loaded to thier full potential,(270-140 thru 160gr/300-165-200gr) as to say that one is So much less recoil, is rediculous unless your comparing a light loaded 270 bullet of extreme light weight (say 100gr @ 2900fps), to a hot loaded 30 cal of extreme weight, (like a 230 @ 2900 fps). In that case, a brake would tame the 300 dramatically.
For your intended purpose, & stated range your golden with either choice. Both offer Way more performance than the needs you stated. Kinda like driving a Corvette to the grocery store, but they're both Sooo cool, it doesn't matter. Both are capable of putting much larger game, at much longer distance in the freezer if the opportunity ever arises. You just can't go wrong with either cartrige.
Id recomend the Winchester Model-70 or REM-700 for nice wood, fit, & finnish, & accuracy, as well as buildability for future use, & Both offer a HUGE selection of aftermarket support, & have good factory tuneable triggers. Fit & finnish tend to lack a lot with many other manufacturers that offer only accuracy. You can find parts, & smiths willing to work on Win-70, & Rem-700 platforms or accurise them anywhere. That's not the case with many other factory guns. Both also offer a bonus over magazine fed guns like Browning etc that severely limit cartrige overall length for handloads of a veriety of bullets.
As stated earlier by Mcseal2, I prefer the 3 position Winchester safety for the exact same reasons, & dislike the REM safety for the exact same reasons. But, my style of hunting includes covering massive amounts of country of all types, thick, open, steep, flat buttes, timber sagebrush etc.
Tree house hunter, or ground pounder spot & stock, REM-700 or Win-70, All of it is subject to personal preference, hunting style, & filling those needs to the satisfaction of individual taste.
