Food for thought: if all carrier fleet A can wipe fleet B out with ease, then B isn't 'well balanced'.
Unfortunately anti-fighter is not what people expect it to be. Sci-fi (and real life to a certain extent) has trained us that the way to counter fighters is with small, point defense laden ships. With the exception of the Omen and maybe Monitor, frigates are hard countered by fighters due to force concentration - they simply cannot survive being swarmed. Similarly, we expect all point defense weapons to be effective against fighters. This isn't the case at all: small ballistic point defense is mostly worthless against fighters and beam point defense struggles to deal enough dps unless massed (luckily beam pd can be massed to good effect.)
What counters carrier fleets are A) interceptors or B) effective anti-fighter weaponry on mutually supporting ships or C) a battleship with good point defense. I don't really think 'dedicated anti-fighter' is needed, but picking up either a dual major or at least a minor in anti-fighter on everything helps tremendously.
A) Is a pretty simple concept: you have a few carriers, those carriers use interceptors, and you use those interceptors to escort your combat ships. You don't need to do the last part, but its extremely effective: your own fighters are immune to your ship guns, so the enemy fighters are getting double teamed, and the main ship PD will shoot down swarmers.
B) effective anti-fighter weapons can be broken down into:
a tier: Phase Lances, Devastators (I haven't tested the new Paladin PD, so I don't know if it falls here)
b tier: Dual flak, railguns, burst pd (with ipdai for flares: c tier without)
c tier: flak, pulse lasers, light assault guns, ir pulse, lrpd, pd lasers, tactical lasers
d tier: the rest
(I'm sure I've forgotten some weapons in there.)
Instead of just putting weapons that are ideal for ship to ship combat, mix in some of these. Then, don't let your own ships run off. Put down a defend command or two (for station fights I like to put one on each side slightly behind the station). When fighters can't force concentrate (IE when they have to run a multi-ship gauntlet to reach the target, or whenever they do a strafing pass find themselves being fired on by another ship) they don't do very well.
Honorable mention goes to the beam eagle: with 2x phase lance (or 3 if you have a good flux managing officer), 6x lrpds, itu and advanced optics (and 3 heavy autocannons for shields) this thing projects a big ring of anti-fighter death. Not as tough by itself against fighters as a Dominator (dual flaks and railguns/lags are tough to beat), but the great accuracy of beams means that this ship will cover all the ships around it out to 1100 range or so.
Bonus points if your officers have Advanced Countermeasures 3 for +50% damage to fighters.
C) is again pretty simply. Either an Onslaught with a ring of dual flak and railguns/lags in the smalls, or a Paragon with pulse lasers/phase lances in the mediums and beam pd of choice in the smalls, will just no sell multiple enemy capital ships worth of enemy fighters attacking it. The Paragon relies on pulsing its fortress shield against strike, while the Onslaught just shoots down everything, from fighters to missiles. Personally I'm a fan of the Onslaught because you can use burn drive to catch everything - no Heron is going to live long enough once its in range to get away.