First of all, it is a muzzle brake, not a muzzle break.
There are a couple reasons why someone would want a muzzle brake on an AR. First of all, on a post-ban rifle we are not allowed to have a flash suppressor on the end of the barrel. If you remove the flash suppressor the rifle doesn't look just right, so you put a muzzle brake on the end of the barrel that looks like a flash suppressor. In other words, some people put them on strictly for looks.
The second reason is the practical reason; to control muzzle flip. Many people confuse muzzle flip with recoil. They make statements like the AR15 doesn't have enough recoil to merit a muzzle brake. Again, the brake isn't there to tame recoil. It is about muzzle flip. Recoil is the force that is directed straight back in the opposite direction of the bullet leaving the bore. Muzzle flip is the force generated at a right angle to the bore. Put a different way, it allows you to fire faster follow up shots because you can get the sights back on target faster than without it. If you want to prove this to yourself, set up some kind of test such as the El Presidente'. Shoot a few hundred rounds on a shot timer using AR15s with and without the muzzle brake. See which gives you the best times along with all your hits going into the A-Zone. The test isn't about just hammering off rounds as fast as you can pull the trigger. It is about firing rapid AIMED shots. You will be firing hammers (two shots with one sight picture) or controlled pairs (two shots each with their own sight picture). When firing a hammer, the distance between the two shots is determined by muzzle flip.
If you doubt the effectiveness of muzzle brakes, don't tell the guys that shoot IPSC race guns. They have been using them effectively for years in handguns chambered for cartridges like .45 ACP, .38 Super, 9x23 etc. Certainly not handguns that give you bone jarring recoil. But, it isn't about recoil, it is about making faster follow up shots.
Yes, some muzzle brake designs make the weapon significantly louder. One of the most famous is the Bushmaster Mini-Y-Comp brake.
I have taken a number of formal Carbine training classes and in these classes pretty much everyone was shooting an AR15 with a 16" barrel. It is kind of interesting to notice the difference between the report and blast of the various carbines on the firing line when everyone is shooting the same cartridge and basically the same carbine.