...PvE - doesn't matter. Just a DPS race, so take whatever. It's too stupidly easy and mind-numbingly boring to be of enough challenge to consider this level of micromanagement and be taken seriously.
...PvP - My vote is on the Runabout. Tractors help in PvP considerably with how often 4 of those things will proc. Combine that with the 360 degree phaser arrays they have for phaser procs (particularly when you and your team run phasers as well) and you get a good number of enemy subsystems knocked offline in a match.
If you're running a healer Atrox, I'd consider shield repair drones.
i'm new to carriers and i would like to hear from carrier capitans to see what you think is the most effective fighters.
i have the doh to get a new fighter class but not sure which one does the best job.
attack ships or repair ships.
Advanced peregrines are best for unshielded targets, given that their highest damage dealing weapons (quantum torps) are wasted against shields. They are especially effective in STFs, with unshielded generators, transformers and gates. They die easily though.
Shield regen units are extremely useful for tanking or helping defend someone.
Stalkers are good for disabling someones auxiliary power. Their shield drain attack is only really useful against low shielded opponents.
Danubes are good at bringing a target to a halt, allowing you to pummel it.
Delta Flyers have a nice shield drain skill.
Basically it depends on your situation. However if we're talking out and out DPS, advanced peregrines easily.