I would bet that if you took 100 .300 WSM rifles and 100 .300 Win. mag. rifles, of the same model and shot 100 groups with each rifle - that the WSM average would be a tad better. Same deal, if you did that with the .308 vs the .30-06, the .308 will produce slightly better groups. Big deal. What relevance that has to killing an elk is about diddley.
They are both excellent cartridges. The WSM is capable of equalling the Win. mag with 180 grain factory ammo - both in velocity and accuracy.
Personally, I never used to have any use for the .300 Win. - until I bought one. I thought that if a person is going to shoot something called a magnum, then it had to have Weatherby on it to be a true magnum. That is wrong - you have to hit what you are aiming at with adequate killing energy, that is more important than who designed the cartridge.
Not sure that Remington chambers a .300 WSM yet, if you are stuck on Remington that might be a factor. I would not sell a Win mag to buy a WSM. But if I was looking for a new rifle in that performance area, I would consider one. Personally, I would buy a Win. mag. There are oodles of factory loads, the military has done all the drops and wind drifts, it is a very good cartridge. If you really want a WSM, disregard the previous sentence and go for it. Launching a 180 or 190 grain bullet at a similar velocity from either cartridge results in the same drops and drift.
The Ultamag and Weatherbys are the next notch up - not sure you need that. More performance but more $ to shoot, also a bit harder to hold onto.