Before I bought the GH2 I read through a couple of posts over at DVXuser.com where some people claimed the motion characteristics to be different of the GH2 vs. GH13 ("strobing"), also detail level and a couple of other things.
Hence, I was curious to make a comparison on my own when I got my PAL GH2 (serial WB01...), so I mounted my GH13 with the hack ("C" settings, and native 24p checked) and the 20mm f1.7 Pancake on top of the GH2 with the 14-140 kit lens set to 20mm as well. I had to use an aperture of around 8 to 9 to get the desired shutter speeds.
Also film mode (smooth), ISO and shutter were exactly equal, resulting in a brighter GH13 picture.
Hence, this gives a disadvantage to the GH2 in resolving detail in dark areas (these areas are darker than with GH13). Still, the GH2 is clearly better in this (and every other) respect.
Summary: to my eyes, the GH2 is a clear improvement in all aspects (IQ, features, ...)