The Perseus does pretty much everything better than the Myrmidon. It dogfights better, intercepts better, assaults better, it just outclasses the Myrmidon on every level. The Myrmidon does nothing well. Besides, if you really want to do anti-subsystem work, you can mount Trebuchets on the Perseus.
(Also if you mount three different kinds of secondaries, you won't have a decent amount of any of them. I usually load out the secondaries on a Myrmidon with nothing but Tempests.)
Also a Prom-S/Akheton or Kayser/Akheton setup would be extremely energy-intensive on difficulties above Easy. Subach/Akheton is the only way to go doing anti-subsystem on the Myrmidon.
As for the Apollo, it's weaker than the Myrmidon in shields and hull, but not a whole lot weaker, has an equal secondary capacity, is smaller and much harder to hit, has much better gun placement (I consider placement of guns just as important as quantity. The Myrmidon's four-shooter is in a horrible position), handles better and has a much tighter turn radius, and is faster on burners.