Sins lacks a whole lot of "Superweapon" options for breaking end game stalemates, but if you use what is there effectively you should be able to break through eventually.
The TEC technically has the most methods, but they are also the most situational. Their Starbase's safety override protocol is the most powerful ability in the game, capable of destroying every frigate and low level capitalships in range (and it is decent). However, the starbase is destroyed in the process and it will take your ships out as well, so you need to be careful with it. The Marza dreadnought's Missile Barrage ability can deal good damage to an unlimited number of targets and will destroy most frigates and a couple of cruisers, and leave the stragglers greatly weakened. They also have the Novalith cannon, which can destroy any planet with two shots that hit close together (unless they have a starbase with a certain upgrade in oribt, but the AI rarely does this). They are also the best suited for attrition warefare, due to their late game economy and build time upgrades, as well as their superior repair cruisers, and their starbase's ability to produce frigates in uncolonizable/enemy gravitywells. Their capital ships can also help out with this, as the Sova carrier's lvl 6 ability, Rapid Manufacturing, increases ship production rates by 250%, while its embargo ability supstancially lowers the enemy's build time and gives you some of his income, and the Akkan battlecruiser, whose armisitice ability allows you to make strategic retreats to regroup with newly produced frigates.
The Vasari have the most fleet destruction methods avaliable, and their tactics can be downright mean sometimes. First and most importantly is phase missiles, which when fully upgraded do by far the most damage of any weapon in the game, and they have several ships that use them. Their starbase, while initially the weakest one, when fully upgraded is devestating and when supported by a decent fleet should be able to wipe out anything, especially as it is the only one that moves. They also have subverters, a support cruiser with an extremely dangerous area of effect ability that can disable frigates and cruisers, effectively making fleets in tight formation sitting ducks. Recently this has become devestating when combined with minelayers, who then lay mines on top of the disabled enemy ships to detonate a minute later, doing massive damage. There Kosutra cannon superweapon doesn't damage enemy planets, but it does act like an EMP against structures and ships, and it also opens a phase stabalizer on the target planet, making the only faction that can conduct surprise attacks (and bypass chokepoints). Also, the Desolater and Kortul battleship also have decent area of effect attacks, while the Skinantra carrier can produce a lot of bombers (usually more useful late game) while healing your fleet at the same time.
The Advent are in a way both the most subtle and obvious stalemate breakers at the same time. Their super weapon, the deliverence engine, is usually of little use and any sufficiently powerful opponent will be able to deal with it even off gaurd. Instead, they rely on simply besting the enemy fleet in straight forward combat, often utterly. They do this with a series of synergies between ships whose combinations can be almost endless. The most common is the "battleball", which sees at least one mothership surrounded by a couple of guardians, with substancial amounts of other capitalships and frigates, mostly Illuminators. The guardians can be used to either use the repulse ability to constantly push enemy ships out of range or shield projection, which allows them to soak up lots of damage from the actual combat ships. The mothership will then start using shield restore, which will recover the shields of both the ships you are attacking and the guardians you that are shielding them. This dilutes your DPS to the point that you won't be destroying anything anytime soon, while the Illuminator's weapons, often powered up with a Halycon carrier, will be tearing through multiple targets much faster. Pretty much all of their capitalships and some of their other frigates can add other deadly dimensions to this combo, but this is the basic version you'll probably end up seeing if you survive the initial Halycon/Illuminator spam. Their starbase also has some powerful crowd control abilities in mass disorientation and meteor control, but you rarely see them used offensively due to the difficulty of getting a starbase up in enemy territory (the TEC get more from doing it and the Vasari can do it more easily).
