Back in the '70s I, like thousands of other shooters, was a big 7mm RM fan. I had a Mod 70 with a 3x9 Weaver and burned a whole lot of H4831 sending 175gr Speer spitzers across the deserts and plains of New Mexico. I thought then (and think now, actually) that the big 7 was the finest long range cartridge for deer, elk, antelope and the like ever made. I shot a lot of game with that rifle and it never let me down.
I always loaded the heavy bullets because in my estimation that's where the advantage of the mag over the other 7mms really comes out.
In a well stocked rifle I can't tell the difference in recoil between the 7 mag and the 30-06.
My then-brother in law had a Mod 70 in .300 WM and we used to argue endlessly over the relative (pun unintended) superiorty of our chosen rounds.
He shot 180gr factory stuff exclusively while I handloaded everything (still do, don't know about him). We hunted together every year for a long time and shot a lot of mulies and a few elk with those rifles. At all ranges I just couldn't tell any difference in the end results; we'd hit a deer and it would become dead. We would trade off once in a while and I could definitely tell the increase in recoil with the .300 WM, but that was the only difference I could ascertain.
If there was a practical difference in trajectory between the two rounds I sure could never tell. We both sighted in at 3" high at 100 yards and held dead on out to 400 yards or so. I could see no reason to shoot the .300 mag with a bullet that weighed only 5gr more than what I was shooting out of the 7 mag. I used to tell my bro-in-law about the 7's better BC, SD, flatter trajectory, blah, blah - he'd tell me that the .300 had more power, had a wider range of bullet weights, would kill a T-Rex at 1000 yards, blah, blah - but in the field there was no difference that either of us could tell. But we'd never admit that to each other unless we were sober.
I sold that gun when I divorced by bro-in-law's sister and moved to the Pacific NW. Living where I do now I have no need for a super long distance rifle and don't own one. An '06 does everything anybody could ask, around here. Besides, super high velocity is over rated in my opinion. In my old age I have come to really appreciate the 7x57, 30-40 Krag and the .300 Savage - excellent rounds chambered in beautiful rifles.
So there's my tale of the two cartridges under discussion. In my experience there really is no practical difference between the 7mm RM and the .300 WM. One shoots a little flatter, one has a little more power, one kicks a little harder, one has better availability of ammo... whatever.
It's a matter of which rifle/cartridge combo a person likes for no really good reason. But we don't need a really good reason for choosing a given cartridge. I wish I could say the same about brothers-in-law.