The short action magnums cost more (more powder, more expensive brass, less barrel life). You want a can or a muzzle brake for them, too. With no muzzle device it can get unpleasant for longer strings or a match for example with 50-150 rounds. I've shot mine in PRS style matches with a can and didn't think recoil was that bad. I've also shot a fast twist .22-250 shooting 90gr VLD's and it's a world of difference, zero recoil-- and that is an advantage.
With some of the higher BC 6mm bullets these days you can probably get similar trajectories (not energy) with a fast 6mm and still get 1500 rounds out of it.
6.5 Creedmoor is vanilla, easy, and it works. Lapua brass, 140gr pills, H4350 and run with it. Ammo is getting to be very common on the shelves, too.
I've shot 6mm Competition match, .260, and now 6.5 SAUM in my Mausingfield. I'm setting the rifle up to be a switch-barrel next and I'm between 6.5x47L and 6.5 Creed for a standard size caliber. Keeping the 6.5 SAUM barrel for the magnum bolt head. I hunt enough that I like the 6.5's over the 6's. I also like the barrel life.
Sorry if this isn't really a clear cut answer. Most everything works, honestly. Just a matter of finding what tickles your fancy.