If you're using a *nix system: https://www.passwordstore.org/ I switched over from LastPass a few months ago. It uses gpg for encryption and supports git for password syncing between systems. Pretty simple to set up and use. There are quite a few third party apps for it already (both desktop and mobile)
`pass` is based on well-established cryptography implementations: GnuPG. GnuPG is recommended by many security experts and used widely by journalists dealing with sensitive disclosures, e.g. the edward snowden documents.
It also doesn't try to NIH some complicated database format or syncing technology but instead uses well-established software (git, plain directory structure and gpg-encrypted text files) which makes it robust, flexible and future-proof, and also responsive to changes in cryptography as it benefits from upstream GnuPG updates. You can use any PGP key structure you want, or even hardware PGP devices like the YubiKey.
KeePass on the other hand seems to be based on mostly homegrown techniques written by people with no or limited understanding of cryptography. (see e.g. [0]) That said, I don't know how much KeePassX continues this trend - but it's based on the same file format so it presumably has to reimplement at least some of KeePass's homegrown crypto.
I don't know how much more convincing you need, but personally I wouldn't even dare consider using anything other than `pass`.
I tried LastPass, but didn't trust them, so I found https://www.passwordstore.org/ some year ago. I can't emphasize enough how good it is, mainly because it is so dead simple and transparent in how it works, and also because it has great bash integration, and uses git which makes it easy to sync between your machines. There is also a firefox plugin that integrates with it, but I don't really see that you need it: it is so easy to use at a prompt.
