His guns and melee skill are the highest & tagged skills so they eventually get to 100.
He can do ok with energy weapons if they're powerful enough but his energy skill is not very high & never goes up so his accuracy with them is lot lower....guns/rifles are his specialty. He does fine with
any bullet gun, doesn't really matter, although companions do have a different movement AI script for pistols/machine guns than for rifles. So what you like him to use is just personal preference. Sniper, All-American/carbine, high dmg. pistol, cowboy repeater, and on and on.
The weapon you give him has to do more dps than his default rifle/what he's already using (based on his skill levels, not on yours - and the game menu shows you dps based on yours, so just give it to him and see if he equips it). So if you want him to use a specific weapon, sometimes you have to remove any other weapon (or its ammo) that's more powerful, from his inventory. Oh, also related...the ammo itself can have an effect on dps, so if he doesn't like a weapon with regular cheap-o ammo he might use it if you give him higher dmg ammo. Weapon mods that affect rate of fire may do so as well. Silencer mods do not work on companions.