What kind of project? I've been using them both for documentation gigs, the major hickup is the lack of 25p on the GH2, I have to shoot in 720p50 or 1080i on the GH2 for easiest conversion, still it's not at smooth in post as I'd want it to.

None of this necessarily has to be an issue though, depending on the project.

Matching the footage color-wise can be a bit of a hassle and the difference is obvious when it comes to noise / mud. Downscaling 1080p footage might give a bit of leverage when it comes to handling the noise / mud of the gh1 - but also for increased sharpness. But this also depends on how well the footage needs to match. Mind, there are also pretty big differences in how different lenses perform on each of the cameras, in my experience. For instance, my 35mm ssc f2.0 looks brilliant on the gh1 but distinctly un-exciting on the gh2. Likewise, my 50mm f1.4 c-mount canon looks a bit too soft on the gh1 but just perfect on the gh2. In other words: if you want similar looking footage you're better off using a softer lens on the gh2.

IMO, the differences are mainly down to the sharper image of the gh2.

The GH1 looks great at 42 Mbps. Higher bit rates on the GH2 can lead to more noise along with stability and import issue. True they are tricky to match I feel its because there is more noise in the greys on a GH2, which also makes it look sharper. I just wrapped a 6 day shoot with 2 GH1's and a GH2. The GH2 was hacked at 66Mbps and it produced allot of noisy images in the grey scale. Several of which I could not use as there was way to much noise to match the GH1's.

A good way to get around footage matching problems would be to have distinctly different pictures on each camera. For instance, only do tele shots (close ups, details) with the gh1 and wide shots with the gh2..
Sure, there's still temperature differences in the colors (even with careful matching) but you can then direct the cameras in such a way that the differences are less noticeable for the viewer.

Rigs: I'm a bit surprised that you find the gh2 noise troublesome in comparison.. I think the types of noise grain is very different and gh1 noise is a lot more disturbing for my eye. But then again, I have no idea what you shot, how you shot and how you plan to use the footage so.. I'm not going to argue against you. :)
Maybe you were just talking about the differences in noise (if you mainly shot with the gh1) - in which case we agree.

Footage matching example:
GH1: 100Mbps Max Latitude Patch Native 24p FHD
GH2: 66Mbps AQ2 Patch 24H

Yep, those frames were shot at high ISO with ND filters. GH1 can't match the GH2 in shadow noise.

@LPowell Thanks for the samples. That was always my Pet Peeve with CMOS cameras. The shadows are always smoothed over and lacking detail. I would first notice it on leaves (I always thought it was a green color thingy). But since VK started hacking this camera it has not been an issue at all.