Like most all have said, any of em are good choices...so you are splitting hairs a bit. I guess you may need to provide a little more info for a better answer. Are you looking for a 7-8 lb rifle that you shoot 100s of rounds a year? If so, the 300 mag may be a better fit. Will it be a bone-stock gun or a re-barreled rem 700? If you don't mind a slightly heavier gun, hope to shoot the heavier for cal bullets, and are gonna practice but not shoot 100s of rounds a year the 300 RUM may be fine.
If its the latter, no offense to Scot but, I think some of his "cons" begin to shrink quite a bit. In other words, if its more of a hunting rifle and not bench rest/TONS of practice you aren't going to be replacing barrels or chasing lands anytime soon. Find a good load and keep it, do some practice and even the RUM will last many years. Same with loading components - no biggy either way if you aren't shooting it just a ton. Recoil: get a muzzle brake
. The RUM won't be bad especially in a heavier 9-10 lb rifle. My 12 yr old daughter killed a deer and elk with my 300 Dakota last year without a brake just fine. It's about a 11-12# rifle though. I wouldn't wish 90+ grains of powder (RUM) on anyone in a 7# rifle for any length of time. If you want a light gun go for the 300 mag.
Not saying you should choose the RUM, just that a little more info would be good. If you shoot it 300+ rounds a year Scots "cons" should bare a little more weight. Also, if you are like me, you get it thinking 500 yds and within a few years that changes to 700-1000. For lighter bullets 180 and below I think you'd be much happier with the 300 mag - vs blowing an extra 15-20 grains of powder out the tube. Personally I compromised between the two 10+ years ago for a 300 Dakota. Have thought about re-barreling, but even then it would probably be one the improved Weatherby rounds or the Norma. Just seems to be a sweet spot efficiency-wise, but you NEVER find rounds in a store for them. Totally splitting hairs now. The elk isn't gonna know if the 180 or 220 grain pill came from a 308 or a 300 UM, especially at 500 yards. Good luck.