I gave Boone an AM rifle, judging by how much ammo he used he got about 50 shots off before it was completely broken and he threw it away. Long before it was completely broken I'm sure it had reduced damage. If it wasn't for Boone saying he the weapon was spent and he was throwing it away I wouldn't know to even look for it. Throwing it away is really annoying since I can always repair them myself.
It's just not worth giving followers decent guns or energy weapons compared to their unbreakable infinite ammo default weapon. Not only do you risk them throwing away a valuable unique weapon, they eat threw ammo far quicker than I do. I gave one follower Pew-Pew-Pew and 20lbs (200 shots) of energy ammo and that was gone pretty quick. Traveling the waste land especially, they'll fire non-stop at distant enemies they have little chance of hitting.
Good melee weapons or a power glove don't seem to degrade and don't use ammo so they are worth giving to a follower.