I have a soft spot for bi-colour birkins. It adds the extra oomph to the bag, and is so much more special. That said, the moment it comes with the contrast piping, the bag becomes a "fun" bag. This opinion is also shared by my store manager and my SAs. I have a birkin with contrast piping, and I use it very casually.
My next birkin, I hope to have is one with a contrast lining, but the piping is tone on tone.