The biggest benefit I see to KeePass over LastPass is sync/cloud choice. LastPass I file in the category of password managers [1] that are more new-user-friendly than KeePass because they directly handle cross-device sync on their own cloud offerings.

However, I like the flexibility to use any "file sync" tool I want to pass KeePass files around between my devices (or none at all, depending on the threat model of individual password files). That opens up flexibility to use things like Keybase File Share and Resilio Sync Encrypted Shares where you have additional options in in-transfer and at-rest encryption of your files.

[1] In that category some security-minded friends that I trust have done their own research on the subject recommend Dashlane over LastPass.