How Microsoft's Surface Book compares to Apple's MacBook: Let's play CPU detective

Microsoft clearly had Apple’s MacBook and MacBook Pro in its sights when it designed its radical Surface Book. But was it marketing hype or was Microsoft really laying down legitimate smack when it said the Surface Book offers “twice” the performance of a comparable Mac?
It very much depends on the hardware that’s inside the Surface Book. There’s not much public information on the exact parts inside the Surface Book—but we do know what Microsoft is claiming.L