I had the same question as the original poster years ago. When I graduated and got my first job out of college, me and some buddies planned an elk hunt. Seeing the only centerfire rifle I had at the time was a 30-30, I went shopping. The local gunshop I frequented had a NIB tang safety M77 in .338 (this was in 2001; this particular shop had LOTS of old new stock). I put a 3x9 Vari-X II on it and haven’t looked back. If that exact gun would have been in .300, I would have bought it, put the same 3x9 Vari-X II on it and not looked back. I can shoot it well and it has done right by me. Is that to say a .300 or 7 Mag wouldn’t have done the same?
I will say that the only elk I’ve ever killed with it was a 60 yd neck shot using 210 NP’s, heck my 30-30 would have worked for that, so I can’t comment on the performance differences between the two (200 gr Speer HotCores do a number on Texas whitetails though!).
Like was mentioned above, getting a tag and finding the elk is the hardest part of this game. And, as a wise man once told me, the most important piece of equipment when hunting elk are the keys to the backhoe.