The differences in gas systems have to do with the length of the gas tube (and therefore, the location of the port). Generally, the longer the gas system, the lower the pressures inside the receiver and the softer the recoil impulse.
The following is generalities, if you want specifics with numbers, it's easy enough to find on the internet.
Carbine length- 7" length, developed for the 14ish inch barrel of the M4, so when you run it on a 16" barrel, you get really high gas pressures in the receiver due to the longer dwell time (the time from when the bullet passes the gas port to it exiting the muzzle). While it works just fine, it also tends to be a little rougher than longer gas systems on 16" barrels.
Midlength- 9" length, basically was developed to match the 16" barrel. The shorter dwell time means there's less gas being shoved down the tube into the receiver and it's at a somewhat lower pressure, giving an easier recoil impulse.
Intermediate- I forget how long this one is, it isn't often seen, but was developed for the 18" barrel length.
Rifle length- 12" length, for the good old 20" barrel.
Another variable is the size of the gas port- a smaller port can cut down on the gas entering the gas tube, minimizing the disadvantages of the shorter systems. Likewise, with a longer gas system on a shorter barrel, a larger port can give enough gas to cycle the rifle (I have a 18" barrel with a rifle length gas system, and it cycles well and is nice and soft shooting).
As said, if you have a carbine length gas system barrel, I wouldn't swap it out (I have one, and I haven't). If you're buying a new rifle or upper anyway, then I'd recommend a midlength over a carbine for a 16" barrel, but it's hardly the end of the world.