Ruatha,
Your opponent has the strongest fighter design.
Rocket pods reach max strength with Missiles III. Adding shields/armor will help, but it sounds like his fighter stacks are bigger than yours. Increasing the stack may help some fighters getting through.
As was stated, PDC are the way to go for killing fighters. Kills Bugs Dead!
What is remarkable to me is that you actually have large fighters! ...and you are fighting other fighters with your fighters!
This seems like a rarity to me. By that time in the game (the research investment to get to large fighters), it seems like ships/fleets would be so awesome, fighters would be a mere distraction.
For me, Fighters:
Early game - very useful
Mid game - useful until PDC becomes common
Late Game - very rare
