Hi, I have both of these lenses and they have very different uses. The 300 comes into it's own when light levels are low, or when I need maximum reach, as it takes a 2x TC well to give a 600 f/5.6
On the other hand, the 100-400 has the benefit of zooming. I have frequently had problems with the prime being a touch long, as subjects move about, so I end up cutting part of the subject off. The 100-400 could simply be zoomed out a bit to get the better framing.
I love both lenses and will often have them both at the ready, on different bodies, so that I canuse the zoom when I need it, or the prime when that is better.
As for IQ, yes the 300 is better, but not dramatically so. The difference is clear when pixel peeping, but once processing is finished and the image resized for output and sharpened, it is very hard to see any difference in sharpness in the finished image.
I would place them very close in terms of IQ when the 300 has a 1.4xTC on it, although the edge would go to the 300 still. However, you would have to pixel peep pretty closely to see the advantage. In real world usage, you are unlikely to see a sharpness advantage.
On the other hand, the bokeh of the 100-400 is pretty crap, and the 300 has it solidly beaten there, with the difference being clear in the final image too.
The 300 is the better lens, as you would expect, but not so much so that I would stop using my 100-400, particularly when I need the extra versatility.