The main reason I haven't adopted Zotero is their lack of a Android app. Something like that on the road map for JabRef?
[1] https://play.google.com/store/apps/details?id=org.zotero.and... [2] https://forums.zotero.org/discussion/110371/available-for-be...
I guess the main difficulty might be in regards to how you store the file links and associated files.
I think the dev do not work on it anymore, but it's in a very usable state and open source.