I think Web Authentication will slowly make U2F obsolete, in a sense that U2F will become one of many authentication methods, others could also be implemented. Checking WebAuth specs one can see references to Android attestation, TPM attestation so generally secure hardware elements. Implementing a U2F solution would require emulating USB exchange I guess.

Of course U2F still has an advantage that you can take your token and authenticate on a different device but unfortunately newer Yubikeys do not support U2F over NFC and there are not so many other solutions.