Mendeley is supported by Elsevier, closed-source, and has premium-only features only for institutional users. Its publisher affiliation is important, when you see things like "Mendeley supports responsible sharing."

Zotero is the full package, GPL, the only premium service is extra data for syncing with their server (not necessary if you only have one client). None of this Orwellian hinting about keeping researchers from using libgen.

It's an Elsevier product, so no interest there.

I'd rather just use JabRef http://www.jabref.org/

They are direct “competitors”. I find Zotero more power-user-friendly. For instance, there is a powerful bibtex plugin for Zotero that can run a server on localhost, so I can fetch the up-to-date bibliography for any particular collection from a make build with curl. I don’t see this hapenning ever in Mendeley

But unlike mendeley, it doesn't send you email advertising for PhDs based on the papers you have been reading it (getting it totally wrong I might add)

according to wikipedia, zotero was first released around a year before mendeley