I've never shot the 120-300mm, but have seen tons of amazing images with it here on POTN and Flickr. I do (presently) own the 100-400mm GM and regard it as pretty amazing. Based on what I do know here are my thoughts:
1. The 120-300mm with it's f/2.8 aperture comes at a (literally) very heavy cost. 7.47 lb (3.39 kg) is way too oppressively heavy a lens for my interest and realistically becomes very limited use for handheld photography. A monopod or tripod would be requisite for most shooting imo.
2. Although it's labeled 120-300mm it has been documented pretty well that it's only about 270mm at the longest end. Not a huge deal, but this multiplies when you add a 2x and it's only 540mm and not actually 600mm. That said, I don't know what the 100-400mm GM's longest actual focal length is - whether it is actually 400mm or close to it.
3. 120-300mm has a beautiful bokeh for a zoom - the 100-400mm GM can't touch that.
4. The 100-400mm GM is insanely sharp, on par with the massively expensive (and heavy) Canon 200-400L.
I absolutely can understand the appeal of the 120-300mm, because it delivers wonderful images. But for me this is an easy choice because the sheer weight of the 120-300mm with the adapter makes it a very unpleasant lens to actually use in practice. If it's not enjoyable to use, then I am much less likely to use it.