If that's the direction you want your career to head in, I'd stay. If you're not joining the organization in the role you want your career to head in, you're risking marginalizing yourself on a path you don't want to be on. So, even though it's more money and a well known organization, you're sending a bit of a mixed message. That said, I'd probably use the interview process as an opportunity to make a connection and put my intentions out there.