My group handles some weapon differentiations using aspects permanently attached to the weapon in question... for example, a shot to the head from a Barrett .50 cal isn't going to make you any more or less dead than a shot from the S&M 500 at point blank range... or really, any less dead than a tank round to the noggin... the difference between them is exactly how much head is left, and at that point- you're the one person in the world who doesn't care, as a character- it's just storytelling from there.
For purposes of determining overall weapon value, we count any such aspect attached as being equivalent to a +1 weapon rating (after all, it can be tagged once for a +2, but after that, is no more useful for enhancing damage than
I'd put a 50cal at weapon 4, but attach a couple aspects to it for <LR Scope> (useful where extreme accuracy or ranged penalties apply) <BFG> (massive damage, split target damage for killing the guy behind the guy you're shooting, or compel against the player who's trying to conceal it), and maybe some special loads.
I'd put the 500 at weapon 4, but attach <Concealable> (I assume, the picture doesn't REALLY make it's size clear, but it looks small enough to at least attempt concealment), and again, maybe some special loads.
A Main Tank Gun, I'd put at Weapon 5 or 6, with the note that it automatically affects multiple targets at that value and ignores all but the most serious armor or cover.
I also let my players attach single use aspects to weapons as appropriate (my melee guy can put a <Honed Edge> on his blade that, IRL, would go away the first time it's used, and my gun-monkey can really hyper-tune his gun's sights or cold fire the weapon like snipers do- first time it's fired though, the vibrations alone screw up such tuning and the bullet ruins the cold-firing)... but that really just amounts to a maneuver they do on the individual weapons that I allow to last until used because it's realistic.