Well, it's an interesting question. Dangerous trade routes. I guess to compare the ships you may want to approach this from a different angle than just by looking at numbers on paper/spreadsheet.
I would ignore the escorts for now, as the aim is to compare the ships. With escorts you can hire an armada and the ship abilities may be ignored.
Also, I would assume that we are talking about a random encounter, i.e. a "pirate" or a group of pirates have not planned to target you specifically, since I believe if it is a targeted and planned attack, the kind of ship won't matter.
Now, trying to look at this from a pirate perspective. As a pirate, I don't want to destroy the ship, since I have spent money in preparation and will likely need to do some repairs and pay the crew, so just enjoying your ship exploding isn't going to make me richer. If my purpose is to destroy a cargo ship, then I'm probably an enemy military and I'm disrupting trade communications, in which case your kind of ship won't matter, since civilian vs military fights are somewhat predictable. If I'm a pirate, I either want you to pay me to pass freely, or I want the ship and cargo, which I can profit from.
To be able to intimidate you I need to look impressive, so that you don't want to fight and rather would want to pay for pass. Likewise, if I have to fight, I need to have an overwhelming force. What do we currently see when we are pulled out of quantum: a couple of Cutlass Black ships, a Connie Andromeda, 2-3 Buccaneers and sometimes a Caterpillar. I would add a Mantis or something what can kick you out of quantum and prevent you from going into quantum again. Mantis and Cat likely won't engage, so your ship is likely to be confronted by 2-3 Buccaneers, 2 Cutties and a Connie.
The ships like Buccaneer and Cutlass don't need to get a ton of damage before being disabled, but you need to be able to hit them, and if you can't hit, it doesn't matter how good and powerful your weapons are. It's similar how you don't bring the Scourge Railgun into Evict Illicit Occupants mission, even though on paper the railgun has a ton of damage. Even a pistol, which on paper has almost no damage, would perform better in this scenario. Also, missiles may be very handy, since even 1 missile can disable a Buccaneer, but many repeater shots may just miss.
The large ships won't be able to outrun smaller and more nimble pirate ships, so there will likely be no escape and there will be a 2-staged fight: ship fight and boarding fight. Therefore, your goal is to take down as many ships as possible before boarding, or even better - prevent boarding stage from occurring. You could try taking down a Mantis to be able to quantum out, but I doubt you will succeed, as the interdiction ship will be hiding.
What would I do if I'm a pirate and I'm engaging you. First, I will try to disable your ship, take down shields and engines. When engaging I will try to attack you from the least protected side.
I believe it also makes sense to look at the nature of the ships, given the lack of information, to try and guess how these ships would perform. All ships have same size components (Large), but different number of them.
So, how these ships are stacking up now:
Starfarer Gemini: A civilian tanker ship, adapted by the military.
A lot of forward facing guns, turrets at the rear and bottom, almost unprotected sides. Engines are exposed and easy to target, as they are placed outside of the hull. Not very maneuverable, so unlikely will be able to do anything once Cutties and Buccaneers get into the unprotected area. The ship's weaponry is likely to work well against a larger target, like a Connie but not against small and nimble targets. The number of turrets may do a quick job of taking down pirates. However, likely that many turrets will create a significant power drain, and with distortion cannons being fired, this kind of firepower may be a disadvantage, as all of them will go down due to lack of power.
The ship has 1 power plant and 1 shield generator, which may be a stretch to keep running, given the number of guns to keep firing and incoming distortion damage. 2 coolers should provide enough cooling for short intense skirmish, but probably won't be able to handle a prolonged fight, given the power drain.
Is this ship easy to board? It has several entry points, making it difficult to control them all. Also, the ship has a layout making it somewhat more difficult to defend, as there are not too many positions where you could flank the boarding party.
Likely the best scenario for the ship is to skirmish and attack first, utilising the impressive firepower, then the remaining pirate forces will unlikely to be able to take you down. If the fight goes into a deadlock, you probably won't be able to last and eventually go down.
Hercules M2: A civilian version of military gunship, repurposed for cargo hauling.
The ships has less firepower, but the turrets are covering front, back and the ship's belly, however, sides also appear not protected. moreover, the engines are placed deeper inside the ship's hull, therefore making it more difficult to disable, still possible however, as parts of engines are exposed. Overall, it seems a pirate has the same difficulty as when dealing with the Starfarer when finding an unprotected area on the ship, but if the engines could hold up for longer, before being disabled, you may have more time to take down pirate ships. A smaller number of turrets may be not a bad thing under a distortion cannon fire, as they may not have a large power drain and be able to keep firing.
The ship has 1 power plant, but 2 shield generators, so it should last longer against the distortion damage. Also, with less guns and less power draw, an overclocked power plant and shield generators may be able to hold a bit longer to give the turrets more time to take pirates down. 1 cooler may be adequate for the components, but under overclocked scenario may not last long, given 2 shield generators.
The boarding defense effectiveness is TBC, as the ship is not in game. Even if it is on par with the Starfarer, if more pirate ships are disabled, it will be easier to defend the ship from the boarding, as there will be less pirates boarding.
The likely scenario for this ship is to try and outlast the enemies, as it's unlikely going to be able to take down many pirates quickly, like the Starfarer. But with the good coverage, and 2 shield generators this may be possible. The ship looks a bit vulnerable though.
Merchantman: A civilian ship designed for cargo haul, long-term stay and merchandising activities.
Can't say much about the turrets and coverage, yet to be seen I guess. The engines are placed in the hull but still somewhat exposed, so vulnerable, probably except the central engine, which sits in the hull. The hip should be able to keep it's engines for a bit longer than Starfarer. Also, can't say much about boarding as the ship is not in game. Also, given there isn't much to say about it's turrets, can't say anything about the likelihood of taking down pirate ships before the boarding begins.
The ship, however, has 2 power plants, 2 shield generators and 2 coolers, all overclocked should result in a pretty difficult nut to crack, so this will come down to how effectively the Merchantman can shoot down the enemies.
The likely scenario for this ship is to do as much damage with the forward facing weaponry, and then outlast the enemies, which should be quite possible given the redundancy. The concern is only 2 turrets, so this ship may be good against larger ships, but for smaller targets it relies on Defender fighters.
Carrack: A military reconnaissance ship, decommissioned and repurposed for civilian exploration.
The ship has 4 large turrets covering top, bottom, front and rear. Also, it has a snub fighter, maybe a light fighter to beef it up. The engines are encased in the ship's hull and not exposed, so likely will be able to run the longest before disabled. With all sides covered with turrets and engines protected, this ship likely has more chances to stay the longest before being disabled, therefore having more chances to take more pirates down. Also, if a light fighter may be fit in, then it could be something like a Hawk, which can use an EMP to disable the pirates, so that the Carrack can take them down.
The ship has 2 shield generators, so should be able to last (also remember the Anvil's trademark tough as nails armor). 2 coolers should provide enough cooling for all the turrets on a continuous basis. The only concern is the single power plant, so power management is going to be required.
It is also difficult to say anything about the ship's layout, but it seems the design supports the boarding defense looking at places and structures you could sue to take cover.
The scenario for this ship would depend on a fighter available. It may be an intense skirmish and then an exercise to outlast the enemies. Otherwise you may try to take down and damage as many pirates as you can, before deploying a fighter.
In summary:
- Carrack looks the most self sufficient (and a Connie is a mini-Carrack): has a complete protection coverage with good firepower, tough armor and good shielding, also can play a wild card, a fighter. After all, this is a military ship is designed to fly into uncharted space with no escort.
- Starfarer Gemini looks like a great skirmisher, with impressive firepower, which needs to be utilised quickly, before enemies can surround you. The armor and shielding don't look as great, and engines are exposed, so try to end fights quickly using all the guns you have. This makes sense, since the ship is designed to be a part of convoy, if attacked, fight back until the convoy ships close in to engage the enemies.
- Hercules M2 looks like a balanced ship with good shielding and armor and a bit less firepower then the others. It has a good firing arch coverage and protection, the encounter may however be lengthy, and skilled gunners may be required to compensate the lack of firepower. The ship is also designed to be a part of convoy, so is likely designed to hold long enough for the convoy to come for help.
- Merchantman is likely to be a very tough nut to crack, but crackable. It may sound counter-intuitive, but the ship may be the most vulnerable of all in a fight against small nimble targets. It will last long, but big guns are for larger ships and there are only 2 turrets, so the ship is likely to fall eventually. The ship is designed to fly with escort, so it loses effectiveness when left one on one with enemy forces.
There are other things to consider, like stealth and route planning. It's best to avoid any fights. Being a recon ship, the Carrack should probably be able to detect the enemies earlier, as well as it could find an entirely alternative route via a jump point that no one knows about.