Cartridge debates are the lifes blood of hunting forums. I love em. But in my estimation the rifle should should be chosen first. Then look at the available chamberings. Within reason of course. It's the rifle you're carrying,manipulating,aiming and ultimately firing at the intended game. If you don't like the location of the safety. The shape or material of the stock. The magazine or it's capacity. You won't enjoy the thing no matter what it's chambered in.
Availabilty of factory ammo is a point I guess. I never found myself in need of emergency ammo. The airlines held my rifle up for 1/2 a day once,but an ammo shortage wasn't the problem. If you are driving to your hunting destination there should be no earthly reason to be without your handloads. Forgetting them on the kitchen table isn't an option. Preference points,license drawings,clothing preperation,loading and sighting in of rifles and ammo. All this and "I forgot my shells"? Not likely. If you fly as opposed to driving there are ways around it there as well. Don't keep your eggs all in one basket.
As for the two choices facing you. Go handle a couple rifles. Remington alone has several models and combinations built around the 300 WM and 300 SM. From a performance standpoint there isn't enough to get too excited about either direction. I like long action rifles and their respective rounds. Sometimes I can make good use of the extra case capacity. Sometimes not. The length of the magazine ultimately dictates how deep I must seat long bullets. I seat bullets in my 300 RUM to function in the magazine. "in the lands" isn't an option. But, it put 3 Nosler 180 Partitions in a 3/8" group yesterday @ 100yds. I'm happy. Buying a factory sporter and expecting to run with a custom long range rifle at truely long range isn't likely eiher. So for the sake of cartridge debate lets keep it this side of 400 yds. Without getting all wound up in drop charts and hair splitting,either round will fill the bill as a big game chambering.
Find the rifle you love. Choose either the 300 Winchester or 300 Short Mag. Tailor the ammo to the rifle. Shoot the heck out of it. Establish your own drop chart through trial and practical range work. If you end up with a friend for life the mission was accomplished. If not.......you get to go look for another new rifle. It's a win win situation