Perhaps the key difference between Mendeley and the other apps is that Mendeley is cloud-based, in that the bibliography exists on Mendeley's servers, as well as locally on your desktop, iPad, or iPhone. Hence, whereas the Nature and PLoS apps consume a web stream of documents, and Papers enables you to sync collections between desktop and iOS devices, Mendeley syncs to central web server. At present this appears to be done over HTTPS. Mendeley recently released an API, which I've discussed at length. Mendeley's app doesn't use this API, which is a pity because if it did I suspect the API would be getting the love it needs from Mendeley's developers.
Like Papers, the Mendley app uses a split view, where the left-hand panel is used for navigation.
You can drill down to lists of references, and display basic details about an article.
The Mendeley app is a PDF viewer, but whereas the PLoS app has page turning, and the Papers app scrolls pages from left to right, the Mendeley app displays PDF pages vertically (which is probably the more natural way to scroll through content on the iPad):
It's clearly early days for the Mendeley app, but it's worth noting two of its most obvious limitations. Firstly, it depends entirely on the user's existing Mendeley bibliography - you can't add to this using the app, it's simply a viewer. Compare this to Papers which can access a suite of search engines from which you can download new papers (albeit with some limitations, for example the Papers iPad app doesn't seem to support extracting metadata via XMP, unlike the desktop version). Secondly, despite Mendeley having as one of its goals being a
research network that allows you to keep track of your colleagues' publications, conference participations, awards etc., and helps you discover people with research interests similar to yours
the Mendeley app lacks any social features, apart from sharing by email(!). I think designing social interactions in bibliographic apps will be a challenge. For an example of what social reading can look like, check out Flipboard.