I am a raw shooter and have a G1, GF1 and GH1. My GH1, even though in the newer manufacturing range (June 2010) and with the latest firmware, suffers from banding in the shadows, even at ISO 400, and I prefer the grain like noise from the G1 and GF1. I asked Panasonic if my GH1 was defective (sent them images) and they said "no". I won't be getting another one, and think the hype around it being far better than the G1 or GF1 for stills is over-played.
That's really strange - maybe the newer GH1s are actually worse (I think mine is around July 2009). I've just pulled up a few images from both cameras at ISO 400, 800 and 1600 in Lightroom, with my default settings of mild sharpening and a touch of chroma noise reduction (no luminance). Unfortunately, I don't have the same images for both, but I've tried to reproduce one or two of the old G1 images on the GH1.
Yes, now that I look for it, there's a touch of banding in large uniform areas of shadow in the GH1 shots at ISO1600, although it's so slight that I've not noticed before. I certainly can't see any hint of this at ISO 400 as I can barely see any noise. If I do some post processing to bring out the noise (sharpening, exposure, contrast etc.) there's certainly no banding in any of the images I've looked at. Other than that, I'd say the character of the noise is fairly similar on the 2 cameras - I really couldn't say which was finer grained.
The biggest difference is simply in the amount of noise - the ISO 800 shots on the G1 look very close to the ISO 1600 shots on the GH1. (I'm not sure which looks better, to be honest - the GH1 looks smoother, but has the trace of banding). Where I can't see any noise in the GH1 ISO 400 shots, I can in the G1, although it's not a problem unless the image is under exposed. For me, the GH1 has pretty much a full stop improvement in noise performance over the G1, which makes it a worthwhile upgrade.