The GH2 resolves fine detail much better than either the 5dmkii or the 5dmkiii. It also tends to retain a little more detail in the shadow areas. But it doesn't have as good of highlight roll-off.
If you want to know more about the GH2 with filmmaking, then you should take a look at eoshd.com where he has all sorts of articles about the GH2.
I prefer the canon approach simply because I already have some lenses for it, and I know that I can keep using those lenses if I change cameras.
If you're doing actual narrative filmmaking, then the autofocus won't shouldn't matter much to you. If you are doing documentary or editorial work where you don't have time to redo a shot, then the autofocus will be very important. But then I would choose a consumer/prosumer camcorder if that were the case and invest in a tripod or camera support system like zacuto or red rock micro.
If you don't need a camera this month, then I might wait to see what the Blackmagic design camera will be like at the end of the month. It's supposed to do everything the 5dmkiii does with video but with a much better image and design for video.
