Alrighty, this looks tasty.
The Manta is definitely unlike other destroyers. The closest comparable (vanilla) hull is probably the Shrike, in that it's a lightweight destroyer with swift movements, that really plays like an oversized frigate. First and foremost, you might see it as a Shrike alternative. It's really cheap for a destroyer - 22,000 credits base, when something like a Hammerhead is 40,000 - but as far as maintenance goes, the ability to field fighters qualifies for a higher monthly supply / deployment cost than you might otherwise expect.
Comparing the Manta to a heavy frigate is perhaps a better option. It gets the benefit of fast movement across the battlefield, alongside a destroyer-grade flux package (and ordnance point budget) and a fighter bay* into the mix as well. Perhaps compare as if it had a medium missile slot or similar instead of the fighter bay, since that's effectively what it sacrifices for the fighters in contrast to other similar ships. The Hammerhead is definitely a better brawler, that can't be denied, but the Manta is more effective at catching small ships and providing supporting fire. The fighters allow it to intercept a target even beyond its own weapons range, and equipping it with an EMP-armed fighter (Thunders or Claws) is a real recipe for rudeness in the Manta.
* It's worth noting that fighters get an automatic speed boost to catch up with their carrier on Regroup mode, so you can put normally slow fighters on it and they won't have a problem keeping up. By that metric, the Manta has another key strength in that it can act as a faster "delivery platform" for slow fighters than other carriers, however this is quite a high-brow exploit and not one that I really care much for.The rest of the weapons package looks underwhelming, and that's true, it is, but the Manta also has pretty good flux stats for its weight - really good in fact: better than a Hammerhead would you believe! 4500 base flux capacity and 280 dissipation, compared to the Hammerhead's 4200/250. The Hammerhead has its AAF of course, which lets it get effectively double firepower for its flux, and it can also use much punchier weapons, but the Manta can actually handle a lot of flux from both weapons and shields. (The 1.0 efficiency shield is to prevent it from becoming TOO good at tanking on the shield.) On top of the flux, it has the Ordnance budget to afford expensive weaponry - Antimatter Blasters are a great thing to equip in the front, and Railguns or Needlers work well in some of the turrets. The wide shield means you can afford a bunch of offensive weapons in those slots, and you can easily negate nearly all PD, especially if you have an interceptor or support fighter equipped.
Finally, Burn Drive is useful both as a dash-in and a dash-out system. AI usage aside, the Manta is great at pulling the "HEY I'M HERE" move, and despite the light status it does still have some armour to take a few hits while the shield is down. Perhaps the ship's biggest downside that hurts its use as a chaser or pursuit craft is losing the zero-flux boost when its fighters are put into Engage mode, but this can be worked around with selection of fighters and/or hullmods.
One last thing: 10 base burn speed. Without any modifications you have a destroyer at frigate burn speed. It's a small thing since we have Augmented Drive Field and Sustained Burn and tugs to worry about, but it's worth noting all the same.
Despite all of this,
the Manta is still only a light destroyer. It can't brawl with other destroyers and certainly can't threaten anything bigger unless you stick some kind of bombers on it. It's very much a versatile, multi-purpose ship design, with the fighters offering the majority of the intrigue there, but all those purposes generally involve beating up small ships. It absolutely CAN perform a harassing task though, but again, this requires particular fighters (don't underestimate the benefit of a wing of Broadswords, Talons or Claws). If you're trying to make a Manta tango with something like a Hammerhead at close range, it won't have a very good time without support. All told, the Manta is an oversized frigate with destroyer-level flux and a fighter bay, and performs best in an unfair fight.
I'm curious to know what roles in particular you've been trying to use the Manta in, and, if you have been using it as a pursuit ship, what exactly you've been pursuing.
Spoiler
The feedback is always appreciated.
And also highly interesting - as per the last time someone had this sort of argument, I pointed out that the Manta is one of the most popular ships in Disassemble Reassemble (it's basically the poster child of the mod), yet we have such a variety of playstyles in this game that it's impossible to create something everyone likes, so if this can't be resolved as an actual balance concern, then I'm afraid that's just the way of things.