It's a funny question, because I actually own all three of these right now! Pirelli's are on my Alltrack, I bought the AS3+ for some new wheels, and my GTI came with DWS06, which have about 5K miles on them.
I have a couple of thousand miles on the DWS06, about 15K on the Pirelli's and a ton of miles on a previous set of AS3+. My general thoughts:
Pirelli's: my least favorite. Handling is OK, grip is good. They're louder than I expected and the rounded shape seems to make turn-in a bit vague. They wear well. They're 225/50, so they're going to feel a bit different, mostly I don't like the shape of the edges. Best price of the 3.
Conti: I have the least miles on these. Noisier than the Pirelli's, though they're 225/40 18's. Still not terrible. Pretty comfortable for a 40 series tire. Handling and grip are good, though they feel a bit vague as well. Worked OK in cold weather and didn't kill me in light snow.
AS3+: They feel like a summer tire than you can drive in all temps. Equal to the Firehawk 500 in dry, WAY better in the wet. Drying through mountain passes in 40 degree rain, I have never had as much confidence in any tire--and this is something I do several times a year. Handling is great, turn in is excellent and they're very predictable. Noisiest of the three, and the stiffest ride. Worth the high price, IMO. Had quite a few miles on my last set and they wore well, still handled well when worn, losing just a bit of wet traction.
For me, I'll probably keep the Pirelli's on the Alltrack, and the AS3+ on the GTI. They're all good tires, but the AS3+ are on a different level in terms of handling, IMO, and one of the best all-around tires available. Performance is isn't far off from the PS4S, but they can be used in colder temps and they wear longer. The big advantage to the PS4S is that they're lighter. It really is that good.
