Source: FSWiki
Hecate: Four TerSlash and one BGreen. TerSlash damage/second: 1925. BGreen damage/second: 6,600. Total damage/second: about 14,600.
Ravana: 2 Sreds (1100 dmg/sec) and 2 Lreds (3,300 dmg/sec). Total: 8,800 dmg/sec.
14,600 Hecate > 8,800 Ravana.
Again, it all depends on positioning, since the Hecate's armament is dispersed while the Ravana's flanks are nearly undefended. Even head-on, however, the Hecate's BGreen is quite powerful and the Ravana would "only" have a 2,200 dmg/sec advantage. Every single one of the beams mentioned has a 4000m range, so range isn't that important, although the Ravana having all its beams up-front helps the Shivans in this department. The BGreen and the Shivan weapons are all direct-fire, non-slashing, so although the Ravana may scrape by in a head-to-head fight, it's at a disadvantage in every other situation. If you position the Hecate at just a slight angle in a bow-versus-bow situation, it would be able to bring even more firepower to bear from its broadside. Through all this, remember that through some odd twist of fate the Ravana and Hecate have exactly the same hitpoints, as does the Orion.
Contrary to popular belief, a lot of Shivan equipment sucks and often they're only able to overpower the GTVA through sheer weight of numbers. The Ravana and Demon are the worst destroyers in FS2.