Why does the P-3 Orion use an engine driven compressor instead of bleed air for pressurization?
The T-56 engine, like all turboprops, is much more efficient at converting fuel into rotational energy than compressing air.  It takes approximately 50-100 shaft horsepower to run an EDC, depending on altitude and how cold of a temperature you select. Bleeding a small amount of air off the engine to run engine anti-ice costs you a 9% loss of SHP, which in flight, would be anywhere from 150-250 SHP.  I don't know the exact volume of bleed air you would need to run a pressurization system, but it is definitely more than the engine-anti ice system.  I'm making that assumption base on the size of the ducting.  The anti-ice tubing is much smaller than the EDC tubing, or the main bleed air manifold for that matter.
All in all, I think it's due to efficiency.  The EDC is more efficient for that motor, but is more complicated and introduces more possible malfunctions.  A P-3 requires a LOT of cold air to keep the computers from overheating, more than a C-130 (same motor) for sure.  I'm not sure if the C-130's back in the day also had EDC's, but they use bleed air nowadays.  So the designers went with whatever can move the most air.  I don't have my Orion Service Digests handy, but I bet there's a more thorough answer in there.  I'll check whenever I go back to work.