The first flash hiders were nothing but a cone affixed to the muzzle, such as found on the SMLE Jungle Carbine and some M1 carbines. They worked great hiding the flash from the shooter, but did nothing about hiding it from the enemy down range.
To hide the flash from anyone downrange, the flash had to be supressed. The common misconception is the flash is unburned powder exiting the muzzle. At first glance, that makes sense because the longer the barrel, the smaller the flash. That extra length is being used to burn the powder more thoroughly resulting in a smaller flash and faster velocities, right?
Not quite. By the time the bullet reaches the muzzle, all the powder has burned to a high temperature, high pressure flammable gas. What causes the flash is actually that gas suddenly mixing with an oxygen rich environment. Longer barrel have greater internal volume lowering the pressure and temperature of the gas before it exits. Although the gas is dropping in pressure, it's still accelerating the bullet until the volume of the bore increases to a point the gas starts losing it's push.
Modern flash suppressors work by dispersing and cooling the hot gas to keep most of it from igniting when it mixes with the oxygen found in the atmosphere, reducing the size of the flash.
I don't have photos handy, but over the years, the list of my favorite muzzle devices has been trimmed rather short.
My favorite muzzle device is a direct thread suppressor, primarily because of noise reduction. There is some flash suppression and, when the AR is set up correctly, reduction of recoil. Some suppressors are better than other with flash & recoil.
My favorite muzzle device for standard ARs is the A2 birdcage. Cheap, effective at flash suppression and offers a small amount of recoil reduction nothing beats it for the money, size and weight.
My favorite muzzle device for shorties is the BRT Covert Comp. It's about the same size and weight as an A2 and it does an amazing job sending noise and more importantly, blast, down range. It's affordable as well.
My favorite specialty muzzle device is the Battlecomp. It's loud and concussive on shorties, enough to make other shooters stop to see what's going on at the firing line. Blast is noticeable even in the sunlight. On a 16 carbine, concussion and flash is about the same as an A2. But where it really shines is when it's used on a well tuned 20 AR. The 20 inch with an A5 RE assembly and the Battlecomp shoots amazingly soft and flat!
Muzzle devices can be a good way to reduce recoil and keep an AR muzzle flat. But they are most effective if the gas drive is set properly first with the correct buffers & springs. For ARs shooting 5.56 NATO ammo, buffers should be H2, A5H2 or Rifle with standard rate springs.
I've tried brakes, but don't care for the blast & concussion. Flash cans tend to be large and heavy enough that I'd rather cough up the money for a suppressor.
That's how we do things, down here in Wolf Hollow.