Way too many imponderables to say definitively. Do they need atmospheric capability? What advantages have been made in propulsion, gravity, and life support? What kind of stealth is available?
I suspect that missiles with a decent AI would almost always be superior to fighter craft in ship-to-ship engagements because you could get higher accelerations and carry a higher payload without having to worry about a life support system. Fighters would be most useful at a far enough range from the mother ship that drones couldn’t be controlled sufficiently fast enough due to light speed restrictions. Which could be anywhere from a few thousand miles to a few AUs, depending on the quality of the AI available and the mission.
First of all, what role do your fighters play? I assume that you’ll have the equivalent of bombers that would be going after the capital ships, and other fighters attempting to keep them out of missile launching radius. You’d probably also have the equivalent of AWACS vessels that would be lighting up the ether trying to locate stealthed fighters.
The only way you’d have actual dogfights is if there were great advances in propulsion technology that would allow the fighters to evade missiles fired at great distances. In today’s technology, I doubt there’s any way that a fighter could carry enough fuel to evade a missile launched. (A space fighter would be much less nimble than an Earth-based fighter because it has to carry oxidizer for the fuel, and life support for the pilot). Even if it could, you could keep lobbing missiles at it until its fuel is exhausted and it’s a sitting duck.
So one possible guess is that future space dogfights would be incredibly boring. You’d sit there drifting in space watching a screen until you saw an enemy fighter. You’d launch missiles and wait. If they hit, you go back to your crossword. If not, rinse and repeat. (I doubt you’d use actual bullets. Even at short range, you have to spray a lot of bullets to bring down a plane. At a few tens or hundreds of miles, you’d have to spray a lot of bullets to fill up the volume significantly.)
The only reason I can think for an actual one-on-one dogfight ala BSG or SW would be if missile defenses were very, very good, either due to stealth, ECM, or powerful anti-missile guns (laser or projectile). In which case, the battles would still be a lot different than in an atmosphere. A ship that’s accelerating would keep increasing its velocity to the point where attempting to turn would require a lengthy burn. A ship could pivot on its axis to shot at a pursuing vessel (using manuvering thrusters), because lack of atmosphere means that you don’t care much about the orientation of your fighter. In any case, I still doubt that you’d ever actually see the other fighter (except for its reaction drive and weapon fire). Probably most conflicts would occur at a significant range and at relatively high closing velocities.
Ah, to summarize, my guess is that space battles would be pretty non cinemagenic. Lots of slow drifting through space punctuated by missile fire and explosions.