Personally I would prefer to break up in person to her face, typically citing in as logically a way as possible the reasons why being together aren't going to work. That being said, any long distance relationship that is going into the gutter is going to be ended online via some kind of skype-like service. I'm not going to wait if it needs to end now. I won't put up some sort of pretense if I have no intention of continuing the relationship in any meaningful manner. Once it no longer works, it ends. Does that require a face-to-face or a message via the internet? Again, I'd prefer the face-to-face, but if it happens to be an internet thing, then that is what it is. Honestly, a clean break is better for everybody, even if they hate you for it.