Compensator = reduces muzzle climb
Muzzle Brake = reduces recoil

Comps have valid applications on ARs, muzzle brakes much less so.  Many muzzle devices are a combination of both.

One thing that is often over looked is protecting the muzzle crown.  If you are using your rifle under and kind of dynamic and/or field conditions (including competition and hunting) there is a good chance you will bang the muzzle on something eventually with the potential for damaging the crown and screwing up your accuracy.  There have been several times when I was glad I had a comp on the end of my barrel for that reason.

As to accuracy, my rifles with comps all shoot 1MOA or less from the bench....don't know what more I'd need for my purposes.

Faster secondary follow up shots are something I really like and believe has practical applications as well.  When the ban sunsets the comps are staying on all my rifles, though I may have sound suppressors made that interface with them for when I really want to suppress flash

Quoted: Sorry, I gotta partially disagree.  TRAINING will do much more for muzzle/recoil control than a brake on a 5.56 rifle.  Heck, there isn't a lot of recoil to control.  Just my opinion.  YMMV. I vote no on all AR brakes.

If this were true, Rob Leatham, Jerry Miculek, Bennie Cooley, Taran Butler, Kelly Neal, and many other proffessional/semi-proffessional shooters would not use comps at all because they get paid to train and shoot and have much more time invested in doing so than probably any of us on the forums here.  Two of those people I named have brakes/comps named after them (both of them are law enforcement shooters too) so they obviously feel it is an important component to increasing ones perfomance with a rifle.  This is not to say that training is not important, just that everything should be viewed as part of the equation for individual performance.