Thoughts:
1) The problem with the fighter carrier is that it doesn't really DO anything.
2) I mean, yes, black omegas, but then if you've got a skirmish point to spend you could split it down at no cost and take paired omega wings. Saying that a skirmish priority ship is good because of patrol priority fighters it carries is just an invitation not to bother taking it in favour of more of the 'good bit' - i.e. the fighters.
3) The guns are weedy pulse cannon. Really weedy - 6 pure vanilla AD.
4) Granted other skirmish level carriers aren't that well armed, but they are better armed than this - the Brikorta packs a heavy laser, the Milani has a combat laser and more AD, the Strike Carrier is about to get the options of twin-linked weapons and/or a missile rack and the less said about the Xeel the better (admittedly the nerf bat swingeth).
5) The problem is that its weapons and psychic crew only matter at close range - but its defences (weak stealth) only helps if its trying to hold the range open. In addition, its three-seperate-battery approach to weaponry means you only get decent firepower if you dive into the centre of the enemy fleet. You might as well take the ship off the board and save the enemy the trouble of blowing it to bits.
6) It's fairly durable if it stays at range. The problem is giving it something worthwhile to do at range; psi-corps already have a superb scout (Shadowcloak) and superlative snipers (mothership and nemesis).
7) Since it already has a fairly prodigous amount of anti-fighter firepower, how about boosting this up a touch and giving it escort? This gives you an escort ship that's well protected from long ranged shots by capital ships (since stealth is good protection from beams and better at long range), which in turn means you don't have to waste your lethal-but-oh-so-massively-outnumbered black omegas and shadowfuries babysitting capital ships, and can send them out to agressively hunt down enemy fighters.
8) The other option is giving it Fleet Carrier. again, a trait which has nothing to do with being anywhere near the front line (which it won't survive and won't contribute anything useful to).