its a matter of preference. i have a quad and 3 thrusters and i prefer the truster set up. quads are fast down the line but i think they don't pivot as well as a thruster. i do like my quad tho on smallish (knee to waist) days that a very racy.
To me quads are basically toned down twin fins, they surf the same sorta way but hold in better and have more drive. Because of this i generally use them the same way i would use a tiwn fin, in smaller fun surf when i just want a different feeling board.
However many people find that they work great in big macking surf too (wardo rode a quad at teahupoo a few weeks ago), i just prefer the feel of a thruster more.