How do you pitch yourself from one BB to another BB?

What's the best way to pitch yourself if you are currently at one BB and are looking to jump over to another one?

Assume that you're in a group like health care and in the new role you would be in tech or whatever. Both roles would be in the same city, same pay.

I'm thinking along these lines: firm culture pitch, more interesting group (and my current firm won't let me switch), better learning experience at new firm, and seeing slower progression at current firm