Maybe what I'm about to write was obvious to all. But just in case:
As I understand it, a "predatory journal" is a journal that will accept anything that is submitted to it so as to financially profit from the authors (and the buyers of the journal, perhaps). Moreover, they are not forthcoming about this practice because that would drastically lower their submissions (not to mention sales!). I would guess that most predatory journals would not want to accept papers of the sort created by Nate Eldredge's wonderful mathgen package: although it did happen at least once, I'll bet that incident was embarrassing (or rather, recognized as working against the game they are trying to play) for the Advances in Pure Mathematics. If that journal published a full issue of gibberish papers, then I think it would seriously jeopardize their profit line and possibly cause them to fold (and yes, get replaced by the next journal, but evidently people like Beall are paying attention not just to the journals themselves but the publishing companies behind them and even the people behind the publishing companies).
Sometimes predatory journals will still publish your paper if you tell them that at the end that you can't or won't pay. I found this strange at first, but I think I understand it better now: these journals want some papers that are actually for real in order in order to acquire a penumbra of plausible legitimacy for all of their papers. At the higher end you get journals most of whose papers are written by real researchers who need their work published somewhere and for various reasons they have chosen not to go through the time and effort of a selective journal. (I don't mean to imply that this practice is not still shady: of course pretending there is contentful, critical peer review when in fact there isn't is highly, highly academically inappropriate.)
What's my point? I don't think there is going to be any uniform sense in which papers submitted to predatory journals are worse than papers published in "real" journals. Demonstrably, some of these papers are real papers. However, if you agree that part of the definition of a predatory journal is that they accept virtually 100% of all submitted papers that are not too clearly gibberish (as well as some that are!), then it would be an amazingly strong indictment of the peer review process not to believe that the papers which have gone through a selection process and are among the X% of accepted papers for some number X bounded away from 100 are going to be, on average, better in every way than papers published by predatory journals.
Is there any evidence of this? I sure think so. Any kind of statistical study is either going to concentrate on a very limited range of journals which need not be of direct interest to any given reader or going to take a massive amount of work. I would rather suggest: select a predatory journal in your field and a legitimate, though run-of-the-mill journal in your field. Page through, say, the articles published by each one in 2010 (or some reasonable subset thereof). First evaluate the articles yourself: can you see the difference? Then look at official reviews of the article (in mathematics there are two internationally recognized services that write reviews of every single math article published -- except that certain journals they drop as not being worth their attention; I believe that similar things exist in many other academic fields). Then track citation statistics of the articles. Is there a difference? Is the difference subtle enough to warrant statistical analysis, or does it just stare you right in the face? I have done a little bit of this practice myself. I am getting inspired to try it more systematically.