For mechs hitting fighters, you want to go all 8th Air Force on them, and cluster up in supporting formations where it becomes impossible for the fighters to attack one mech without taking fire from three or four. Beyond that, there are 100 roles for AA.
Rules 1 through 98 are just the word 'range' repeated over and over, louder each time, so that hopefully even a pet rock will get the hint. To sum up: An aerospace fighter's only defense against ground fire is range modifiers. Nothing else. Therefore, to hit them, you need weapons that can achieve medium or short-range mods at a fair distance. Because of the way lawn-dart rolls work (assuming standard rules), that's all you need. Raw damage is irrelevant, you just need to hit them with something, anything.
Rule 99 is to-hit bonuses. Pulse weapons, flak mods, anything else that helps you in that all-important goal of scoring a hit any hit, and help overcoming range penalties.
Rule 100 is damage. Yes, I know what I said before. Scoring the hit is all-important...but once you know you can, yeah big guns are better for forcing threshold crits. Because nothing drains all hope from an ASF user like just barely making the lawn dart roll...and then having to make another roll because of a Control or Avionics crit.