Destroyers are tech 2 ships. They are useful sub-hunters with effective anti-submarine weaponry, as well as anti-torpedo defenses that protect them from submarines' attacks. They also have medium power direct fire weaponry that can be used to attack other ships and bombard land targets. The UEF and Cybran versions have light anti-air guns with slightly less DPS as well, but better range than T1 mobile (land) anti-air. Destroyers are the toughest T2 naval units.
Each faction's destroyer is very different from the others'.
The UEF Valiant Class has weapons for countering all threats except tactical missile launchers. With powerful cannons (it has the highest direct fire DPS of all the destroyers), and high HP, it is a superlative choice for any fleet. However its torpedoes are mostly ineffective - more meant to supplement its guns in surface combat, and its anti-torpedoes are the slowest to reload. Protect with Cooper torpedo boats if confronted with large numbers of submarines.
The Cybran Salem Class Destroyer is a very useful unit in that it can move on land, albeit slowly. Relative to land units, its high amount of health, DPS, range, and rapid fire make it very effective in countering T1 and T2 units. On the water, however, it has less HP and its guns inflict lower DPS than the Valiant and the Exodus, though this is somewhat compensated by the greater range and higher rate of fire. The torpedoes are superior in all ways to the Valiant's, does more damage than the Uashavoh's, but is more vulnerable to anti-torpedoes, and while technically superior to those of the Exodus, the latter's additional depth charges give it the advantage.
The Aeon Exodus Class has excellent cannons and torpedoes, as well as a torpedo defense. The Exodus can be superior to the other factions' destroyers because it has both torpedoes and depth charges, so if you are using it against a non-hovering naval unit and you are in range for the torpedoes, the Exodus will cause more damage then any other destroyer. Though keep in mind that the DPS of the surface cannon is not as high as the Valiant or the Salem, and its slow muzzle velocity allows micromanagement to effectively evade its shots, so what distance you're fighting at makes a difference. The Exodus's lack of AA demands that you pair this ship with Shards or Infinity ClassCruisers to be effective.
The Seraphim Uashavoh is submersible, making it able to sneak up on an enemy base or submerge when a superior surface fleet shows up. It is especially effective paired with the Yathsou; together they sneak around and surface near vulnerable targets. With the destroyer attacking land-bound targets and the sub intercepting aircraft, this formation can deal with a wide range of threats.