Two different beasts. The main difference in terms of shooting is muzzle velocity, you'll get significantly more velocity at 16" long. The other difference will be recoil impulse and muzzle blast. With a short barrel, there is a sharper recoil impulse and less weight out front to keep the muzzle down. There is also more muzzle blast as the powder hasn't had time to fully expend its energy in the barrel. The longer sight radius on a longer barrel also provides more accuracy over longer ranges if you are using iron sights.
The advantages of a shorter barrel are in weight and maneuverability. If you are doing short range work and will be in and out of doorways and vehicles, then a shorter barrel is a huge advantage. If you are just going to the range and shooting from a bench, then a longer barrel is likely for you. There are also in between lengths of 11.5-14.5" that can give you advantages of both with less disadvantages.