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The advantages are mainly comfort and not disturbing your firing position after every shot. The disadvantage is that you have to put up a hard case between you and the next guy over, at least if you're considerate. Also, some competition classes don't allow brakes.
pro - less felt recoil, alows for quicker follow up shots, can spot your own hits at shorter distance
cons - (these really are more personal then the pros) loud, can annoy other shooters at the range, depending on the design kick up a s**t ton of dirt if you shoot pron.
is it worth it on a 308.. not really unless you find the recoil to much.. a good position negates any real recoil or muzzle hop, on any thing past 100yds, i can keep the target in my sights on my SA, rem 700