I am sure everyone knows BBR has a feature which XMR doesn't have yet (and would require hard fork to add), where each coin is flagged with the minimum # of inputs it will mix with when it is transacted in the future. This enables BBR to avoid inadvertent unmasking of the anonymity.

Well when we consider an attacker do that on purpose, then XMR is much more suspectible to anonymity reduction (which we are still trying to decide if also reveals the private key).