My Dad has 300 Win-Mag and I started on that, I now have 300RUM. As shown earlier the Army is adopting at least some .300 WinMag giving that cartridge a boost. It's already easier to find Win Mag than RUM in some reloading applications. If your LGS carries it is often either both, or a coin flip and they'll carry a ton of one, and none of hte other.
I road Tripped to my grandparents halfway across the country, stopping at every Cabelas on the way, and it seemed like several in the middle of the trip... Idaho through Wyo/Colo area were pretty hefty in the Win-Mag and skimpy on the RUM. Or Vice versa. I forget which, since I have several reload cycles left and wasn't buying. I just remember being whimsically entertained by the incongruity... An actual example of what I'm talking about though would be the RCBS Lube die. You can get one that fits Win-Mag but not RUM. Not that it really matters, you don't need either, because handloading that much .300 would be rare for anyone not in a camoflage clothed members only club in Northern Idaho of... unque... political beliefs.
I'd use either win-mag or RUM in 300 for anything I would hunt in North America. Though I'm unlikely to hunt anything big enough to hunt back. Fair chase is when I chase them, not the other way around.