.308 Muzzle Device

You're not going to find any muzzle device that helps with sound reduction without paying $200 to the ATF. That being said, suppressors are fantastically effecient brakes and dramatically reduce recoil, and you can reduce noise to hearing safe if you get a good one.

If you meant a brake that doesn't up the perceived volume like most brakes do, that's a different story. There's plenty of forward-venting brakes like the Troy you linked to. The only problem is that they're not very effective at reducing recoil specifically because they're forward venting. A brake can work in three possible ways: 1) direct muzzle gas to the sides instead of forward to eliminate or reduce the equal and opposite recoil force of the gas exiting the barrel 2) have baffles for the gas to strike adding a slight forward force and reducing perceived recoil and 3) Venting gas upward so the equal and opposite reaction reduces muzzle rise. A well-design brake does all three. The forward-venting designs do half at best. My advice would be to steer clear of front-vent designs and buy a real brake. I have a JP Benny Cooley brake on my 16" .308 and although everyone around me hates it, there's no perceptible difference in noise from the shooter's position.

The Kies "Blast Master" is very, very similar to the Troy above, but costs less and isn't pretending to be medieval:

http://www.joeboboutfitters.com/KIES_Blast_Master_Linear_Compensator_p/kies-blst mstr30.htm

I have one in .308 on a 300BLK upper and one in .223 on a standard 16" AR upper. It does a good job at redirecting blast and noise forward. There is a modest effect in recoil and muzzle rise - basically it softens the kick - but not much. If noise/blast is your primary consideration, it's good.

I've shot a 14.5" .308 with a brake and it was incredibly brutal, both as shooter and as spectator. Worse than the 50 BMG I shot. I suppose a 16" .308 would be slightly less bad, but only slightly. I can't recommend a standard brake on such a short .308.

You might consider the cage style devices, like the .308 Battlecomp (BABC) and .308 Spike's Dynacomp as an intermediate option that reduces recoil without as much painful blast as conventional brakes.

recoil reduction=BIG increase in loudness. Unless you suppress it= $$$

That said, 7.62 suppressors do work really well if you get a good one. Less blast, less recoil, less dust being kicked up.

It's win-win-win! Of course, you must pay.

BSW

The Delta Brake....

http://www.deltabrake.com/gallery.htm

The JP Recoil Eliminator is the best on the market or close to it. If you want a more traditional profile or to keep your rifle 3-gun legal, I'd recommend one of their Tactical Compensators. I have one on my 16" FAL, and that gun now shoots softer than an AK.

I use the surefire AR-10/LR .308 MB762K MUZZLE BRAKE ADAPTER and it works great on my 308 mil spec Rem 700

It is stainless steel and It works ok with a 24 inch barrel it maybe brutal with a 16 inch.
You can buy it here http://www.brownells.com/.aspx/pid=45547/Product/AR-10-LR-308-MB762K-MUZZLE-BRAKE-ADAPTER