Because you are better than they are?

edit: Since I can't delete my comment now, I just want to apologize that I read your message too quickly and missed the 50% salary difference part. Come on, there's ethical and then there is crazy, of course you leave and take the other offer if it's 50%, that's common sense and any hiring manager should understand it. But that's not really commonplace and you can handle it in a professionally ethical way.