Given their particular usage case, which includes not just shared, synchronized access to secrets but managed, tiered levels of access, it seems to be a bit beyond what I've seen of Keepass.
Extremely. I've been so pleased with Keepass and the security it provides. I'm using a web interface now (https://app.keeweb.info/) which is open source and worth checking out.
Keeweb is pretty awesome, and is amazingly just a static HTML page. If you're comfortable running your own secure webserver, you can self-host that for added security: https://github.com/keeweb/keeweb#self-hosting
The one issue I had with Keepass is that on iOS (and this is Apple's fault!) it is not possible to choose different cloud storage providers to keep the password database file on.
This silly thing alone would preclude me ever buying an iOS device! (My wife ran into it when I tried to get her up and running with Keepass, she gave up...)
I love keepass's simplicity, no browser plugins with pop up dialog boxes or UIs that conflict with the browser's own password management, just, a list of accounts and passwords.