Corsairs have a plus in larger numbers against the Hessians and SCRA. Not so much against the house navies though. For 4.87, the Corsairs have a chaotic pattern of attack: Attacking Rheinland from the north and south (Omega 11, Omega 7 but also Frankfurt and Munich through Sigma 13). Attacking Dublin, Cambridge and Poole through Omega 49 and 50 - but that's mainly piracy raids rather then a military invasion. Bottom line, Corsairs do not have the standing forces to confront a house navy headon in-lore.
And I'm not exactly sure where you got the idea that the Coalition tech is any better then the Corsair tech. Corsairs stole their initial technology from a Rheinland expedition that stumbled upon Crete (and were subsequently thanked by execution). Coalition didn't even have that - any tech they took with them from Sol would be heavily outdated by now.
Wide awake in a world that sleeps, enduring thoughts, enduring scenes. The knowledge of what is yet to come.
From a time when all seems lost, from a dead man to a world, without restraint, unafraid and free.
Mostly retired Discovery member. May still visit from time to time.