Just to point out, the 2 ships most commonly accused of being OP are the Pyramidion and Junker. The only ships with 2 light guns facing exactly the same direction are the Pyramidion and Junker. Coincidence? I think not.
These ships give you easy weapon combos along with respectable maneuverability and respectable repairability. The Galleon is next in terms of guns facing exactly the same direction, but with such a maneuverability problem that it is often left helpless. Spires have guns facing together, but have maneuverability and durability problems. Mobula has guns facing together but has mobility and repairability problems. Goldfish and squid don't have good arcs.
These 2 ships are strong because of the damage type gameplay that GoIO features. A single gun is insufficient (almost) always. You need to blend 2 guns together. Pyra and Junker offer this without serious drawbacks, or rather without drawbacks that can be partially covered with piloting tools.
The fact that these ships have a high skill ceiling and such strong relevance in high level play is a better indicator that other ships are lacking in payoff than that these 2 are lacking in drawbacks.
Consider these 2 ships to be the beginner ships. In a normal game, you beginner ships will be your warrior, your melee type, the average brute. Once you have done well with this you might branch out and try a more skilled character type, like magic or ranged. These types have clear drawbacks, but also the potential to be stronger or more helpful to a team. We have seen teams do this with the Galleon and Goldfish, and a very few teams work it with a squid or spire. Mobulas have also made an appearance.
If these ships aren't doing so well, it indicates that they have insufficient reward for their drawbacks. Like a squishy mage without a powerful area of effect spell, or a weak bard who can barely buff his allies. It isn't that these 2 ships are too good, it's that all the other ones don't have quite enough upside, or maybe a little too much downside.
Consider a random example - take the squid, remove 4/5 of its permahull and add a 4th gun on the front-right of the ship pointed 45 degrees right of forwards. Huge downside, but what an upside. The killing power of the squid would skyrocket, but it would die so very easily. Is that balanced or even a good idea? Probably not. But now the squid gets an upside worthy of its downside - the ability to kill quickly.
TL;DR: Pyra/Junker are fine, other ships just don't have enough upside - buffs/radical changes to ships give more real changes than nerfs of what we have.