I have used both very extensively and can honestly tell you the 300 WM is superior to the 7mm RM on game. The question is not whether you need the extra energy it's a matter of WHEN you need that extra energy the old 7 ain't got it. I shot many head of game with the 7 RM and about 3 times as many with several 300s and the 300s work much better on those less than ideal shots that sometimes present.
I can also say I've used every bullet in the 300s from 150 TTSX to the 200 AB and Partition and have settled on the 200 Accubond for my all around hunting. I also settled on a 300 Wby cartridge but the 300 WM is a very potent cartridge. As far as accuracy goes, that will be more a product of your chosen rifle than the individual cartridge. Both are equally capable of 1/2" moa accuracy in suitable firearms, with properly tailored handloads.
I have also found when handloaded to their full potential the 300 WM offers a substantial margin over the big 7. I had 3 different 300 WM that would give 3100 fps with 200 gn Nosler Parts. Of all the big 7s I've owned and built (7mmRM, 7mm Wby, 7mmX300WM, 7mmX68 imp, 7mm STW and 7mmX300 Wby), the only one that even approached the 300 WM was my 7mmX300 Wby in a Ruger #1 with a 28" barrel and 175 Partitions. The new 7mm RUM equals and exceeds the 300 WM but again doesn't hold a candle to the 300 RUM.
My final conclusion, after building and shooting and hunting with many variations in both bore sizes, is that there is nothing you can do with a 7mm bullet that can't be done better with a 30 cal bullet of the same or better BC and SD. Also there are as good and even better bullets for the the 30 cals as the 7mms, so don't let that argument sway you, it's just not true, there has been more development in 30 cal bullets than ever in 7mm for both hunting and target shooting. 30 cal is the absolute darling of NA shooters and hunters and all the manufacturers recognize this fact.
Yes there is more recoil in an equal weight rifle, this is the law of physics and cannot be denied, but that in itself is telling you that you're also getting more out the front end, again laws of physics.
This has been my experience for what it's worth, I've used 30 cal Mags all over the world and banked some pretty high priced hunts on their ability to perform in the wind and way out there sometimes, and have never been let down, on anything from Suni, to Eland to Bison to Marco Polo to Altai Argali to grizzly and Dall and Stone sheep.
Just a note of interest, the caribou in my avatar was taken with a 7mm RM and a 160 Partition.