fighters do anti-light type damage. they do excellent damage to bomber strikecraft, LRM frigates, and siege frigates but they do very very little damage to anything else.
bombers do anti-very-heavy type damage. they do excellent damage to heavy cruisers and orbital structures. they also do reasonably good damage to capital ships and most other cruisers. they do only half damage to most of the frigates but they have generally higher damage than fighters so they perform reasonably well against everything.
fighters are more the defensive type of strikecraft. they are very good at protecting your fleet and from enemy bombers and LRMS and they are very good at protecting your planets from siege frigates (which will try to bomb and destroy the colony) and LRM frigates (which will try to destroy your orbital structures).
bombers are the more offensive type of strikecraft. they are the most efficient way to destroy enemy orbital structures and they perform very well against enemy capital ships (the best weapon system to attack an enemy capital short of having one of your own capitals). additionally bombers are the only true counter to heavy cruisers, which are otherwise extremely hard to kill efficiently.
both types of strikecraft are extremely vulnerable to enemy Flak frigates but of the two, fighters are more vulnerable. Bombers are more vulnerable to fighters than fighters are to other fighters. both types of strikecraft are extremely hard to destroy with anything except fighters or flak frigates because all other weapon systems miss about 90% of their shots against strikecraft. the exception to this is that there are numerous capital ship special abilities that damage or disable strikecraft in a large area.