Refraining from sending passwords plain text along your transport is always a good idea. Even if on the public internet the password's transport may be encrypted, once it hits your network it might not be. HTTPS accelerators (or reverse proxies) will remove this secure layer and with basic authentication you'll be left with the base64 clad password.
While you could argue that if your local networks are compromised you're screwed anyway. (think bad network topology in your data center) Think back to defense in depth, I'd rather the passwords never enter my network to begin with. (Think digest, or better yet Kerberos.)