Both Bitwarden and KeePass are very secure, certainly much better than something like Lastpass…
Bitwarden’s server and client are open source and completely E2EE (similar to Signal, the server is zero-knowledge). And even if you don’t trust Bitwarden’s official server, you can host your own.
KeePass is fine too, but it doesn’t have a centralized server like Bitwarden. You have to use other tools to sync your vault between devices. Which some people prefer, but others dislike. Just depends on your preference.