It depends on the situation.
Fighters kill scouts, siege frigates (most things destroy these) and long range frigates. However, their true purpose is to kill bombers which they do very well. Fighters are the only units that counter bombers.
Bombers destroy structures, starbases and cap ships.
Interesting points, all of them I find to be correct. But really, you shouldn't even launch fighters if the enemy has flak frigates, bombers will be ok, but I don't recommend it. I don't tend to use squadrons myself unless the enemy has ABSOLUTELY no capability to defend hemselves against them, that means, no cap ships or light carriers that can launch fighters, and no flak frigates. When that happens, which it usually does, thanks to my Kostura
, I call in about three heavy carriers, two full of fighters, the other full of bombers, and five light carriers (remembering, they are all escorted with attack cruisers, and this is a late game situation), three with fighters, two with bombers. If the enemy has SB(s), then I use more bombers.