All of the short mags are exellent cartridges, with that being said. You mentioned 300 yards and beond , which I have done with two of the chamberings mentioned. I have shot mule deer beond 300 yards with the .270 WSM and the .300 WSM. The 7mm WSM would work just the same but I can't speak for it yet, I have stocked my 30" Shilen barreled action chambered in 7mm WSM as of yet. But I can say the 7mm WSM is the ballistic equal to the 7mm magnum. It does it with less powder, less recoil and in a lighter package.
Out to all practical hunting ranges, in capable hands all three with the right bullet weight will work but when you start talking elk, big black bear etc at extended ranges I would be reaching for either the .300 or the 7mm WSM. There is a huge selection of bullets for either that will handle such a chore. Now between the two, 7mm WSM and .300 WSM. If you were to throw them in the boxing ring together for over all performance at 300 yards and beond, when it comes to energy, wind drift, tragetery. The 7mm WSM is going to be the one on top.
A 7mm WSM with a 160gr Accubond at 3100 fps, which is easily done with a 24" barrel. With that bc and speed it is a hard combination to beat for just out right killing stuff. Then againg for all practical hunting ranges all three are a exellent choice, but for all north American big game within in standard hunting conditions, I myself would be picking up the .30 cal.
For the all holds bared, take off the gloves, down right nasty long range big game slam fest at distance. When it comes to the short action chamberings, I'm going to be running a 7mm WSM and a 180gr pill.