They are very similar, but not the same. I'll try to give a basic description, and if I don't get something quite right, I'm sure someone will clarify. I don't claim to be an expert, just another enthusiast.
The PWS uses a true "long stroke" system, where the piston is attached directly to the bolt carrier by means of an operating rod.
The Adcor uses a hybrid short/long stroke. The actual piston is not attached to the op. rod, and impinges only momentarily on the end of the rod.
I prefer the PWS system because it most closely matches the tried-and-true AK-47 style of action, with all the ergonomic benefits of the AR. I've read that this action has a longer dwell time, which helps cycle the action more smoothly. As I perceive it, the gas has more time to "push" the piston/op rod/carrier assembly before the excess is bled-off through the vents in the op. rod sleeve. This set-up also helps keep the BCG in a straight line, thus avoiding the infamous "carrier tilt disease" that infected some first gen. short-stroke designs.
The Adcore is more like a short-stroke system that uses a permanently attached op. rod to avoid the carrier tilt. Almost every other short-stroke has a separate op rod that slams into a "strike-face" on top of the carrier. Adcore attaches this op rod to the carrier, similar to the PWS. but the piston still slams into the end of the op rod, unlike the PWS. I don't like all this "slamming" going on. I'm no engineer, and there are lots of very respected companies, with real engineers, that swear by the short stroke system. It is certainly the dominant design out there.
I just don't like it. Why have steel slamming on steel when it's not necessary? Why add a bunch of springs to the hottest, most active part of the gun?
The PWS design just seems like the simplest, most logical, and least likely to malfunction. For the life of me, I have no idea why they are the only ones using this design. (If you don't count the dozens of foreign militaries fielding millions of AK's that have been going strong for over half a century now.)
This is just one man's opinion. Your's may differ. Keep in mind that there's nothing "wrong" with either system. There's nothing "wrong" with the original DI system either. I just wanted something that I could run lots of cheap, dirty ammo through and not have to spend more time cleaning than shooting. If accuracy is most important...you should get a DI system.
Do some more research and pick the design that makes the most sense to you. That's what I did when I ordered my first PWS. I'm so satisfied with my decision that I just ordered two more uppers that should be here next week! After that, the rest will be DI...
ETA:someone beat me to it. serves me right for walking away before i hit send