The 50mm 1.2L is, no doubt, a great lens. I also have the 5D Mark III and use it for video. I do not have the 50mm 1.2L, but I do have the 24mm 1.4L, Canon 50mm 1.4, and the 70-200mm 2.8L IS USM II (among others).
I and others prefer Zeiss lenses for video. The advantages of Zeiss lenses over the Canon lenses are mainly in usability for video, noting that most video users manually focus:
1. Zeiss lenses have hard focus stops. The focus ring will stop at infinity and at the minimum focus distance. The Canon's that I have will rotate past infinity and min (you can feel it, but the ring still moves easily).
2. Zeiss lenses have long focus throws. My Zeiss 85mm 1.4 will go about 270 degrees from min to infinity (my Canon 24mm 1.4L has about 180 degrees or a little less), and the 70-200 feels even less, making precise focus manually a little difficult (not impossible, just not as easy).
3. Zeiss have all metal build, including most of the hoods. For some, this may be a negative, as Zeiss lenses are heavy - though it isn't clear that this isn't due to the glass.
Finally, the image quality is arguably better on one or the other. I personally prefer the look of the Zeiss lenses, which makes the decision easy for me. In fact, our Canon 24mm will be going on the selling block soon, to be replaced with a Zeiss.
Now, for photos, that's possibly a different story, as the Zeiss are manual focus. Having said that, the 5D Mark III will confirm focus with the Zeiss ZE lenses.