I like Keepass becuase it is not tied to any ongoing subscriptions or providers. You can use the file sync tool of your choice to distribute your file. The downside/feature is not having tight browser/app integration.
Yeah KeePass is great! I currently use KeePass2 on my Trisquel 7 machine. I use that app in conjunction with Deja Dup to back up my password database to S3. There's even an app on the fdroid store called KeePassDroid but I've yet to make it work. I think the version on the store hasn't been recently updated.
Integrations and plugins exist, and for me, browser integration was easy to set up.