Many people have no idea what the difference between the following:
A) Flash Hider
-A.1 Blast Cones (Subcategory)
B) Muzzle Brake
C) Compensator
As a rule of thumb, you cannot have all three (as least not well...).
A) As the name suggests, it hides the muzzle flash. To preserve night vision, prevent 'flashlighting' of your position.
- A.1) Blast cones will generally do an excellent job of hiding flash from a 270+ degree viewing angle, but many still have flash when seen from down range.
B) Reduction of recoil by redirecting the forward travelling blast of gasses not forwards. Simple physics. As a consequence, they will be louder in whatever direction the gasses get thrown. How 'blasty' muzzle brakes will be depend on the design.
C) Reduction of muzzle climb or 'flip' by venting gasses in an upward direction, often by closing the 6 o' clock vent/hole/baffle/etc. Very useful for rifles that do not recoil 'in line' with the shooters shoulder (i.e. M14 vs. AR15). Does NOT mitigate or reduce felt recoil. Passive advantage of reducing ground disturbance signature when firing standard prone positions.
For example, a standard A2 muzzle device is both a flash hider and a compensator. It does not reduce recoil.
Competition brakes like the Benny Hill Rolling Thunder, various Miculek devices, etc. maximize reduction of recoil and muzzle rise at the cost of 0 flash hiding and often extreme lateral concussion. Some muzzle brakes will do a very good job reducing recoil while not being 'excessively' blasty, like the KAC Triple Tap and the BCE BattleComp.
Blast cones like Noveske's KX3 or the SPEX do not reduce recoil or muzzle rise (aside from the added weight

), and they do a pretty good job of reduce flash but their primary purpose is increasing the comfort of people in proximity to you by forcing all the blast downrange.