1) If it's what you want to do, then by all means, you have to leave. Find all the schools that offer that degree and then compare till you break it down to one.
2) It depends on where you are going. Having a badge would be a big plus. One of my best buds had to leave our school (financial reasons) and transfer to Kansas State. He didn't have any problems affiliating with Beta Kappa, and now has 2 badge numbers. Plus he had a great time