One game that I've played that allows for great weapon customization is Blacklight: Retribution. You can choose the receiver, barrel, muzzle, scope, stock, and magazine. There are at least a dozen options for each part. The parts are also fairly balanced. You can make a low-spread and recoil AR at the cost of damage or a high-damage AR at the cost of recoil and accuracy. We can also enhance this by allowing the addition of, say, chips/mutators that change a specific part of the gun. And from my time playing BLR, everyone has a different gun.
I've also heard a lot about the game Loadout, which sounded pretty interesting with its weapon customization. I didn't actually play this game but I'm sure that somebody could tell you about it.
These are my half-baked ideas.