Hi Neils
I've been using the GH3 with the 100-300 for 16 months now. Prior to that I was using the 100-300 on the GH1.
It's really difficult to see any difference in sharpness or quality between images taken with the GH1 and those with the GH3. In fact I think the GH1 images are in some cases sharper than the GH3 images. This may be due to the higher resolution of the GH3 out resolving the lens. This is all the more frustrating as I also moved from the 14-140 GH1 kit lens to the X series 12-35. The 12-35 is a fantastic lens. It's very sharp and shows what the camera can do in terms of sharpness.
So if your main purpose for upgrading from a lesser camera to the GH3 or GH4 is to improve the quality and sharpness of images taken with the 100-300, don't upgrade. You won;t see an improvement until Panasonic improves the quality of the lens. I also noticed some funny business with the ISO in the GH1 compared to the GH3. I think the GH1 iso 100 is the same as the GH3 iso 200.
One thing that improved the quality of my images (both GH1 and GH3) was moving to the pro version of SilkyPix. They had an offer last year for Panasonic users to upgrade to the Pro version from the Pany supplied version for $40. The pro version has better noise handling and a neat feature for enhancing darker areas with dodging or HDR.
I maintain a photo life list and this gallery has the new adds and upgrades for 2014, all taken with the GH3 and 100-300 combo. Sometimes conditions or the timing isn't the best so some images may be lacking in quality but they still represent the best that I've been able to achieve for that species. The images are best viewed in full screen (double click the large image).
http://www.paultavares.smugmug.com/Wildlife/Birds/AU14/i-MhHPfzs
Paul