I'm using keepass, and the sync does not seem to be hassle - my file lives in dropbox, and it's always been synced before I open the app on another device. Bonus - backing up the database is as easy as copy-pasting a file.
I'm glad to read this, as I hit upon a similar solution for my own password store. My Keepass DB lives in Dropbox, but my key file does not. If I want to open it (along with password) on a device, I manually install the key.
I'm sure I forgo some convenience by not having field auto-populate all of the time (Keepass can do some of this, but I haven't had it work reliably), but I relax knowing I need not worry about a third-party service being hacked or my credentials being behind a paywall.