As typical for recommendations beginning with "just", this entirely ignores a critical concern of the problem domain - in this case, the phone sync use case I explicitly called out in my prior comment. Jabref looks
worse than Zotero in this regard; where the latter fails but at least makes the attempt, the former shows no sign of bothering to try at all.
I'm a hobbyist student of hymenopterology, not a professional researcher; this is an interest that needs to fit into a life with many competing concerns, rather than the work my professional life is built around. It should not be a great surprise when tools built for and by professional researchers fail to meet my needs - to say nothing of those tools being built to a typical academic standard of software quality, something in the implication of whose existence I am being quite generous.
I don't yet know whether Jendeley is any better, but it could hardly be any worse, and having been built with modern tooling and in a modern HCI paradigm offers significant promise of justifying my time and interest. (And as I do find things about it I don't like, it won't require software archaeology to fix them!)