Well, part of it is that they are different technologies. The way a Canon camera autofocuses for pictures is different than how it does in Live View, and video uses the Live View technology. Canon would have to adapt the SLT technology with a translucent mirror to auto-focus in the exact same way a Sony does. In doing so, they'd give up all the photographic advantages of the mirror, which isn't worth it. Basically, the Nikon autofocus sucks because it doesn't use the focus sensor (due to the mirror being up). I doubt Canon will have solved this in a way that makes it comparable with what sony has in their SLT's, let alone what the FS-700 has.
Sorry to tell you, but the NEX 5n does NOT use SLT technology. NO SLT, NO phase detect sensors being built into the imaging sensor like a Nikon J1/V1. The Sony NEX 5n doesn't use any form of phase detect for focusing, none, zip nada.
The NEX 5n uses contrast detect auto-focus, just like the quick focusing Olympus cameras. If Sony, Olympus and Panasonic can build good contrast detect auto-focus, why do you feel that Canon is so incompetent that they couldn't