ETA: Also, I've just tried using the standard Klingon carrier and it doesn't seem to give the kind of punch along with it's fighters when compared to my Vor'cha Retrofit. What kind of playstyle I should expect to adopt when using carriers when compared to cruisers and science vessels?
It's more of a support role. You could try going for a drain build. Use powerdraining Boff abilities and support with powerdraining drones.
I think it's the Dacoit Flight Deck cruiser that has the best powerdraining pets, but simple Power Siphon Drones work well too.
In an elite STF, a good drain carrier can leave an elite tac cube nothing more than a helpless heap of metal in space.