I had the original EF 300/4 L for ten years. I used it alongside the EF 70-200/4 L and Nikon 400/2.8 AI-S. It was sharper than the zoom but not as sharp as the 400. However, I always found it to have virtually zero CA, unlike the old 400.
CA was increased with the use of the EF 1.4x but was easily corrected. The teleconverter had no noticeable effect on AF.
I sold it in favour of the original EF 300/2.8 L but in my comparison tests, and subsequent similar images, I only see a marginal improvement in IQ and AF. I was hoping the f2.8 would be more useful with the EF 2x II, but while IQ is exceptional, the AF on my current DSLR is only 20% successful.
I often think about the possibility of returning to the far lighter 300/4 L for easier handheld photography.
While it is extremely useful to know how one's lenses, of different focal lengths, compare, one can't forget that they have different uses. When you fill the frame with any of these three lenses the results will be equally superb. Rest assured, the EF 300/4 L is a very good lens.
You need to ask yourself if you need a lens between the 200 and 400, and perhaps even if a zoom somewhere in there may be more useful than the prime. Of course it also depends on how much you use the 300mm focal length.
Good to find you on this forum!