I actually have a GH2, and yeah it does have a form of zebras, as well as peaking. I find that the stills it takes aren't great at all, but I love it for video, especially after I hacked it. It also has noticeably less moire than other DSLR's, but rolling shutter is still an issue.
Also you are correct in that AVCHD is h.264 just inside a Mpeg transport system, so they are very similar codecs, but in my opinion AVCHD is the better codec, especially if converted to Prores as it just holds up so much better in the editing process, and is very noticeable in grading.
I just think that DSLR's have been getting a lot of hate recently, and yet I don't see why. They obviously aren't for someone brand new to filming as it is an expensive investment, but I think someone with the money and skill can produce astounding work with a DSLR, and personally I see them as holding more creative potential than straight up video cameras because of the ability to swap lenses. This is from personal experience as I have worked on both prosumer video cameras, like the Canon XF100, which is the camera one of my friends has, as well as DSLR's like the GH2 as well as 60D
I love them both, and the XF100 is actually much easier to use and yet still produces a fantastic image, but with knowledge and skill I just feel the creative potential of DSLR's is much more, and can produce amazing shots.