I do, I've been a heavy user of both for 4+ years, but I'm not a security expert of any kind.
LastPass has been exploited a few times in ways that could have given up passwords. Their UX and server infrastructure seems to be a mess of php scripts, that itself doesn't have to be insecure but is a code smell. Their commercial support looks unmaintained. Both platforms support "cloud" based syncing but since 1Password's is pretty new I can't speak to it.
1Password does local encryption outside of the browser, LastPass will encrypt locally in the browser.
1Password can leverage other file transports to sync passwords, iCloud, DropBox, or any shared directory. LastPass does it all with their servers.
LastPass's web interface if compromised can have you give away the password to all your passwords. 1Password has a much smaller risk of this and would probably have to include a malicious software update.
1Password Families/Teams exists and I'm not familiar with it but it probably has a similar attack vector to LastPass's web interfaces.
You know, they both offer end to end encryption with similar attacks. Overall these companies are big targets and I'd rather keep my passwords offline or synced via side channels in a standalone app like 1Password.
PS I'd be amiss if I didn't mention dashlane https://www.dashlane.com/ I hear good things and it's passed review at a few companies who know their stuff, but that's all I know.