If I could hit a target equally with all of them, the gun I'd choose would be based on 1) flatter bullet trajectory, which would decrease my chances of making a mistake if the distances and wind change from optimal, and 2) weight of the gun, which would matter if I had to carry it for a long time.
If you shoot all those rifles equally well then I'd look at which rifle best suits what you're hunting.
When I looked at your caliber selection I was initially attracted to the .257 Weatherby, big .257 fan, and the 7 Mag. None of the choices are bad however. I'd select the one rifle I'd want to have, that shot the best, that I wouldn't mind carrying for ten days of backpack hunting with a shot at sunset on the last day.
Me, I pack a .338 Win Mag for a coues deer hunt because that's my one rifle for all game. Not the best as far as distance shooting goes, it mirrors the 30-06 in trajectory, but it's the rifle I shoot most so that's my choice. I know it, have shot it a lot, and have no doubt it will work. While I have other calibers, even a 6.5 x 284, which would be a grand mule deer caliber, I opt to carry my old friend. Someone I know has the same attitude about his 30-06 and another feels the same way about his 7 Mag. It's more about being familiar with your chosen rifle and knowing it as you know your own hand.
Pick one and get to shooting. Mule deer season will be here soon enough and good luck!
Vince
