I hunted with a Remington 700 stainless/synthetic in 7mm SAUM for a few years after its introduction in 2002, from Texas to northern Canada, taking several species of big game up to 400+ pounds. It just about duplicates the .280 Ackley Improved (which I've hunted with some as well) in powder capacity and ballistics.
But I never could see any difference between the way they killed big game and how the .270 Winchester killed big game--and I (and Eileen) have used the .270 a LOT. In fact at one point in the 1990s I'd taken more big game with the .270 than any other cartridge.
Have also used several 6.5mm cartridges on big game, rising in case capacity through the 6.5 Creedmoor, .260 Remington, 6.5x55, 6.5-06, 6.5 PRC and .264 Winchester Magnum. Never have been able to tell any difference in the way they killed big game and the .270 either.
What this partly means is over 50+ years of hunting big game with a wide variety of cartridges I keep seeing less and less difference in how various bullets of the same basic weight-range kill stuff--or even bullets somewhat outside of that weight-range. There can be some difference in "hittability", whether due to recoil levels or trajectory (including wind-drift) but the biggest factor has always been where the bullet lands, and how it performs after landing.
There's nothing I'd hunt with a 7mm SAUM that I wouldn't hunt with a 6.5 PRC, so if forced to choose between the two rounds the decision depend primarily on brass and ammo availability. I doubt the supply of either will ever be nearly as abundant as for the .270, but many rifle loonies just have to have something different--partly so they can argue about ballistic minutiae.
