I've used a 7mm for years and love it. The 7mm and 300 win is debate that's will always have half like the 7 and the other like the 300. I just bought my first 300 for hunting season this year so I can say either one is a great choice.
I personally shoot a 7 Mag as well, but the majority of my hunters bring a .300 as the most common caliber i see. I like them both and will definitely be buying a .300 WSM someday soon to have in my arsenal. The 7 Mag doesn't usually provide the "knock-down" power like the .300, but it also doesn't kick like a .300. That being said, when an animal is in your sights the kick really never matters. You can't go wrong with either. The nice thing about the 7 Mag is being able to shoot 150+- grain bullets for smaller game like antelope and deer instead of heavy grain bullets that tear up a whole shoulder of meat.
cant go wrong with either one. .300 will have more recoil so alot of people would pick 7mm over it for that matter. both will do the job and do it well
I would rather shoot a 300 in a 175gr. bullet then a 7 mag in a 175gr. bullet as far as recoil goes. But , you have 2 very good calibers that will do fine. 300 offers a larger range of bullets from 130-220+ there are some smaller bullets available. 7mm mag range from 110-175. If you reload you may find some different grain bullets out there.
Can't go wrong with either i use the 7mm mag and in two years I've taken 2 cow elk and three mule deer. It's got more than enough power for what i need it to do.
They both will get the job done as said. Which ever one you shoot the best, take it. Take a little test. Have one of you buddies there, close you eyes and have them hand you one of them, then the other. Keep you eyes closed, which one is the most comfortable. Take it and shoot it and then shoot it some more. I think you will have your answer.
How often are you going after elk size game or bigger? I would have no problem taking anything with my 7mm Rem mag; except a very large bear. Either one will harvest an elk. Pick one and put good optics/rings on it and hit the range.