I have an 06' GT and my son has an 07' V6.
In my experience:
All Body Parts - I upgraded my son's to a Roush front bumper/GT grill and rear wing.
All suspension - I replaced just about everything w/GT parts; good to upgrade brakes/rotors/shocks/sway bars from a GT though you may not have anti-lock depending on V6 model. The brake lines on the GT won't swap to the base V6. Never tried to retro-fit anti-lock. Not worth the effort IMHO. No experience upgrading rear end/drive shaft. I've also heard the transmissions (auto's) are slightly different but never verified for myself.
I wouldn't try swapping major electronics (ECU's, harnesses, connecting blocks) as they're specific to a V6 though many of the ancillary items are exactly the same (i.e. switches, controls, seats, lights, some minor harness pieces, connectors, etc.... Not sure if GT speedo may work; never tried it). You would have to check part numbers/application to be sure. Outside of V6 specific engine/drive train and electrical pieces I estimate a good 60% - 70% of a GT car will bolt right up to a V6. These cars were made to be modular.