On the topic of Gas Guns, the 6.5 Grendel will out shoot the .308, and that depends on the shooter too. JP makes great stuff but you can't compair the 223, 6.5 and 308 Gas Guns to other calibers, that is why there are differnt classes for guns. If the PRS lets you use what ever you want, even the 6mm is more accurate and reaches out further than a 6.5 Grendel. BUT, the Grendel and 308 are also good for hunting and I would grab a Grendel over a .308 any day.
JP is coming out soon with there Gredels, is shows that on there site, and I imagine it will be way more accurte than many out there. My Grendel just off a bench at home shooting for fun, I drill 3/4" MOA at 100 yards all day long. Take time and you can do that at 200 yards and bang 6" steel targets at 600 yards with no problem. Many people shoot the Grendel out to 1,000 yards easily. Super Sonic to 1,250 yards with 123gr projectiles.
So a 308 will work, but they are heavy (AR-10 platform) and lots of recoil. The AR-15 platform is much lighter and the Grendel is one of the top calibers for long range shooting and hunting. Also the Grendel is out there in bolt guns too but that is where personal preferance comes in. I vote for MSR's (Modern Sporting Rifles, AR-15 for the newbies).
I know people who are going from bolt guns to MSR's because of hunting with them is on the rise and that is a big factor in using them more these days.