Hmmm, tough call
The one in the book feels like it should be great... it has all sorts of cool systems and stats.
But it has (ah, MT, how I love thee!) errata galore. And even without it, you still have the classic 'he brought a single laser turret and a weak hull to an SDB fight' problem. Uneven forces really are and death will usually ensue for the weaker, slower, etc. Skill can only go so far in this respect and in MT, I found it not so far.
I like Mayday, but it handles only CT ships and bringing MT ships over is tougher than you'd like to think.
I like HG, but its not an RP fight system. Similary, neither is Power Projection:Fleet or PP:Escort. Those do larger fleet fights well, but just aren't great (IMO) for small ship fights. HG particularly with the 'close range, open range' tends to not bear much similarity to realspace fights in every space sim I've played, which end up being jousts. Or slow broadsides. But not both.
Then we have Brilliant Lances. Brilliant game, excellent detail, PC ships that can actually do something (because the whole setting is about small ships generally). OTOH, does not translate other ships into that system well (I tried and tried to make MT ships work, but it hurt me more and more... I gave up).
So what does that leave? Not too much.
The system you need is probably a narrative one, but there MT helps you. Look at the numbers for the ships, let that guide you in what sorts of things can happen, and then let rolls and PC skills play it out (in a narrative way, without obsessing with details). How will your PCs know? If you can't figure out the ship combat tables, they sure aren't likely to.
MT gives you a great skill system to handle initiative and to handle task resolution from firing, to dodging, to damage control. So do it in a narrative style, moreso than a literalist tactical boardame style.
The type of ship combat I'd really like to see is one from the old Star Trek RPG adapted to Traveller. In that game, various PCs took different bridge positions. The idea was every player should have something to do in the fight and decisions to make and things to track. And it worked well for that aspect and it was so-so as a fighting game (balance wasn't 100%, but it worked well enough).
We need THAT sort of a multi-player-involved tactical narrative system for running fights, moreso than we need another gearhead mess of errata that only really lets one or two players do anything in a fighting turn and requires lots of table lookups.
So I'd go with the narrativist approach. The game is what its all about. If you use colourful damage descriptions, makeup task for patching hull holes, getting airtight seals shut, stopping atmo leaks, working on damage repair as anyone with a tech skill, trying to rescue trapped people with the battle dress (greatest damage control tool ever is the powered armoured exoskeleton), and so on. Let the pilot dodge and be evasive. Let the navigator try to cut the corner to slingshot the planet. Let the gunner try to shoot out the larger ship's sensor cluster or master fire director.
The players won't care if the game is a fun one; The details of a table heavy, errata laden morass aren't what they come to play for (in most cases).
If you have to pick a system, and you have standard CT ships in the MT world, go with Mayday. Otherwise, stick to a narrativist solution that keeps most players involved doing something during the fight other than just sitting waiting for the ship to blow up.
I have some pretty good coverage here of non-combat operations, but you'll notice the section at the end trails off... where combat is, because I never did have time to work out a great MT combat system. But maybe some of the non-combat stuff will help enhance your game...
http://traveller.kaladorn.emwd.com/ad_astra_per_aspera/knowledge_base/rules/starship_ops.html