Hey all. I'm eyeing the Canon 50mm 1.2L, but am also considering the 85mm 1.2L for some portrait photography. I do see a lot of posts about the 85mm not focusing as fast, but being very sharp, while the 50mm focuses quite quickly but isn't as sharp as the 85mm.
What does everyone suggest? 
You didn't really specify your main use for the lens. - The two lenses have rather different uses, and I believe your intended use, rather than the characteristics of the two lenses would probably be a more important factor in determining your choice. The 85mm is intended more for head and shoulders portraits, while the 50mm is a normal lens, which has a fairly wide range of uses.
I would take the approach, once you have decided whether you need a 50mm or 85mm lens to look at the available lenses in either focal length, and then choose from those, based on your individual requirements.
For instance, if you shoot a lot of group portraits, an 85mm lens may prove difficult to work with. On the other hand, if your intended use is mainly for individual portraits, the 85mm might be a better choice. I assume you currently have zoom lenses that cover these focal lengths? If so, have you done any analysis of your existing work to see which focal length you use the most?
Once you have chosen the focal length you require, it is worth considering the Canon L and non-L variants, and also possibly even Sigma and Zeiss (if you can live with manual focus).