I've recently migrated from Mendeley to Zotero. I first had to downgrade Mendeley because recent releases also encrypt your local database to guarantee lock-in [1]. Quite scary.
I've used Zotero regularly since 2012 or so. At the time I chose it because it integrated with Firefox, though I recall looking into Mendeley as well. If you use BibTeX or BibLaTeX I'd recommend the following extension: https://github.com/retorquere/zotero-better-bibtex
I'm very glad I never even tried Mendeley given the database encryption fiasco. Mendeley put a blog post out saying that preventing importing to Zotero was unintentional, but I don't buy it.
Before the database encryption fiasco, I would recommend Mendeley and Zotero if someone wanted a citation manager, but now I recommend staying away from Mendeley as much as possible.
The only major problems I've had with Zotero were related to Firefox's switch to WebExtensions. Now adding a copy of a webpage to a citation is more difficult than before the switch, though probably equally difficult as in Mendeley.
Zotero has been great. I switched four years ago and never looked back. Plugin support is great- I have drag and drop support in my latex editor and fairly easy citation selection in Lyx
I love zotero, and would never switch to Mendeley because of the lock-in problem, but the lack of any mobile apps is a real problem. Reading and annotating on an iPad is a key ability, and the 3rd part PaperShip is buggy and no longer under development.
[1] https://www.zotero.org/support/kb/mendeley_import