This is a great discussion topic.
In my humble opinion, the answer to this questions is going to lie ultiamtely with the paintwork which you are working on, and if the user's of the machines are highly skilled, to see the differences in most cases, its going to be a cause of getting out the microscope...
But here's my thoughts:
On the majority of paints, unless you get out a microscope and really peer at the finish achieved the difference is going to be nigh on impossible to see... But: it is there.
On softer paints, in dark solid colours, is where the fun begins. Having seen my own, and oter detailers who I hold in very high regard, finishes using the PC, I would have to personally say that the rotary has got a very slight edge when it comes to finishing - proving its been used correctly. The constant rotation seems to break the abrasives down more evenly and this results in perfect clarity, crystal clear finish. Personally, all my best finishes have come from the rotary, but using myself as an example isn't really fair test as I might just be better suited to the rotary than the DA... However, from the finishes I have seen from other detailers, this seems to hold true for them all, the rotary finish being ultimately the sharpest and clearest.
The PC on the other hand doesn't quite seem able to break the abrasives down quite as thoroughly - it breaks them down for sure, and you get a great finish but look very very carefully and on some paint types (the soft ones which are more senstive to the abrasives) and compared to the crystal sharp rotary finish, the PC has got a very slight micromarring. Now this is oh so very slight - and on the majority of paints you just wont notice it - on hard paints, you wont see it and on metallic finishes the flake generally hides it. But on a soft solid colour (red's my favoruite test colour for this), you can see this very slight difference andn this appears to be independent of the user of the machine from the finishes I have personally seen.
With that in mind, ultimately for me the rotary is the king of the finishing tools. The PC is excellent, of that there is no doubt and a skilled user will turnout amazing finishes and unless we get microscopes out, on the vast majority of paints we wont see a difference between the two tools. What I would do is if you own both tools, get yourself a solid dark coloured scrap panel, with a paint type that is soft to medium - polish one half with the rotary to the best finish you can, and then try and match it under magnification with a free rotation DA such as the PC... A fun way to spend a few hours...
