The OP asks a very good question. Does the 6.5PRC provide any “real-world, hunting advantage” over the 6.5CM at practical hunting ranges? Have to admit, I have a 6.5CM that’s throughly impressed everything I’ve ever pointed it at - yet, after the 6.5PRC came out I bought into all of the ballistics-hype and bought one as well. Do I regret the purchase? No. It is a fine shooting and well crafted rifle in its own right, but I regret the reason that I bought it. I bought it for hunting, but based the purchase on recommendations from long-range shooters, ballistics studies and folks who are into ringing steel at 1k. My hat is off to them and I respect their expertise, but that’s not how I’ll be using the rifle.
Like many on this forum I have more rifles than I can get around to using regularly. But my 6.5s were specifically purchased for hunting sheep, goats, chamois, ibex and other mountain game. My CM loves the 143gr ELD-X and 140gr NAB - both have proven very effective on game. In the mountains wind speed and direction can vary quite a bit between my shooting position and where the animal is standing. So, I like to keep my shots on game to 500 yards and under. I’ve taken a number of critters between ~300-500 yards with the 6.5CM - many were DRT and the others didn’t go far. So, for reasonable mountain hunting applications the 6.5CM has proven itself. Field-ready, with scope, covers, sling, and full magazine, my CM is still under 8lbs, very well balanced and handles like a dream.
For Tur or other East Asian hunting where 500 yard+ shots are not uncommon the 6.5PRC might be a slightly better choice as it will buck the wind slightly better and deliver a bit more energy at those longer ranges. Also, maybe it is because I was primarily a bowhunter for a big portion of my hunting career I’m a firm believer in relying on hunting skills to get within reasonable shooting range on game. Pushing the envelope via long-range shots are better fodder for bragging rights, but I feel increased confidence when stalking to within 300 yards or so, and there is a much lower chance of an errand shot.
I have a Yukon Sheep Hunt in August and am currently debating which rifle to bring = 6.5CM vs PRC. While I know my trusty CM will certainly get the job done, the PRC has never been on a sheep hunt so it is tempting me. Do I believe that the outcome of my sheep hunt can be negatively impacted by my choice of which rifle I take? Not likely due to the cartridge, but the PRC is 1/2 pound heavier. I’ll shoot both a bit between now and then (including mimicking field conditions) and will likely end up taking whichever I feel most confident in.
My 2 Cents
Imo - take the one you trust on a hunt like that. Break the PRC in on a more routine hunt.