Mendeley = Elsevier = Evil incarnate. If you care about universities and their libraries you cannot support Elsevier.
Their iPad app is pathetic anyway. No freehand annotation support, your notes are trapped in Elsevier's evil servers forever. There used to be a third party app called Papership to do freehand annotation, but it's been discontinued.
Papers is currently the most capable app. And it's a little less evil than Mendeley. But only just. poster above is right that updates have been troublesome since v.1. But the original developers have all fled the company following acquisitions. This may mean that the original beauty of Papers might be lost, but also hopefully their original incompetence when it came to updates.
Papers is in the process of merging with ReadCube, which has a terrible Java style pathetic app on the Mac and no real iPad support worth mentioning. This is potentially a disastrous move, and they are running 6+ months behind schedule with the beta program, which doesn't bode well...
Zotero is of course the ethical choice. But they have no iPad app. PaperShip has been discontinued. I truly wish there was a workable iPad client for Zotero.
--> conclusion: it's a terrible scene. I think about this *a lot*, and my 3000+ pdf and academic book library has never fully recovered since the death of Sente (which used to be the best reference manager for Apple's ecosystem) a few years ago. At present I use Papers but it's a very very shaky platform.