Why aren't many people using the Galaxy Class Ships in STF's and PVP? I can tell you a couple reasons. One is that the cruiser is crippled by a very slow turn rate tha doesn't make since, because the are larger ships that out turn it. Another reason is that it has no modifiers, thus bringing no benefit to owning one. Just bringing sauser separation is not a bonus because it doens't boost anything for you and many ships not can separate, and their pets have more effecttive support tactics than the Galaxy Sauser. This Cruiser has little DPS properties so its very hard to do alot in Elite STF's and since torpedos barely put wear on shields, the ship is difficult to be affective in PVP. The Galaxy attracts the most attacks in PVP not because its the biggest threat but its the easiest target or kill. This is due to the lowest deffense: turning too slow to rotate a facing shields, not being able to get attackers off your stern, and not being to dish out damage that would deter attack for being in so bold and close.
I am a Tac Captain who is still try to faithfuly fly my Galaxy to represent true canonism and weather the difficulties of using it in this game.