Drag’n’drop / copy’n’paste from EndNote results in a temporary in-text citation that looks like this {Nadkarni, 2012 #1714} (note that this is a real EndNote citation that I just dropped this text box).
In Papers, you choose in preferences whether it will insert a temporary citation like {Nadkarni:2012eg} or the full reference (see below for the full reference). After you complete your paper/thesis/article/academic-masterpiece, you compile to Word (or other word processor) and then use the relevant software plug-in to convert the temporary citations to properly formatted citations and the reference list.
Does Mendeley have a similar feature?
UPDATE: I’ve just watched a short video on Mendeley here. It looks like Mendeley attempts to create the “proper” citation first go, which means that (a) you can’t tell which citations were added by Mendeley and which were added by you and (b) could prove troubling if you add more references later.
If you want a similar feel to the pop-up window option that Mendeley uses, try Papers 2 as it offers something similar that does work with Scrivener. Papers has come a long way and seems to offer most, if not everything, that Mendeley does. Although not free, it does have an academic price which seems reasonable (I bought it when a student, and paid for the upgrade a few years later - if the upgrade had come 12 months earlier, I may not have used EndNote at all).
I have a love-hate relationship with EndNote. I love the fact that my university offers it for free. 
Actually, EndNote has also improved dramatically. While it is still ugly and, at times, confusing, it is much more stable than it used to be. Also, it is mega-powerful compared to Papers (or any of the other reference manager apps I’ve investigated over the years). Because of its power, I was able to edit its templates to correct some minor errors in the way it implemented APA style (actually, I edited an edited version of the template I found from a New Zealand university). Note, however, that I don’t use EndNote’s cite-while-you-write feature in Word; that just seems to be a recipe for pain and distress, which is also why I didn’t like the video demo of Mendeley. That approach seems fine for short works but not, to my mind, pieces that are tens of thousands of words long.
If you like editing under the hood, EndNote is good. If you like simple and understandable, I think Papers is awesome and worth investigating. Phrased in a way that does not favour any individual reference manager, if I had to choose between my reference manager of choice or Scrivener, I’d swap my reference manager without question.
Reference
Nadkarni, A., & Hofmann, S. G. (2012). Why do people use Facebook? Personality and Individual Differences, 52(3), 243–249. doi:10.1016/j.paid.2011.11.007