Length of the barrel also plays a big factor. There are a number of rifles that are chambered for larger pistol ammo (.357 and .45 LC) and they have a good deal more velocity when shot from one of those.
Obviously the .22 LR is going to have less powder in the casing (and thus be slower) than the 5.56 mm NATO round, despite the fact that the bullet itself is virtually identical in size (only .003 of an inch difference in diameter).
But, all this is minor, compared to the real answer to the starting question:
A bullet is slightly slower than Superman.
I was waiting for someone to say it.