Both are based on the same underlying principles (AES encrypted database, encrypted using a slow hash of the master password). Both have been audited professionally. Both have browser extensions whose source code you can read (it is JavaScript, just open the extensions directory). Both support a full array of 2F options.
People are moving from LastPass to BitWarden because it is a better product. Plus many dislike LastPass's owners due to the LogMeIn pricing/business practices (like difficulty cancelling/early cancellation to avoid additional billing/aggressive sales people/etc).
The only advantage BitWarden may have is its backend is open source software and you can run a copy yourself (although most choose not to). If you're running it yourself BitWarden is likely your primary contender. If you aren't the difference is largely academic.