400mm debate: EF 200 f/2.8L + 2X TC III or RF 100-400 f/5.6-8 ?

Question is what gives me the sharper 400mm image?

Not counting the versatility of the zoom, what gives me the better image at 400mm?

In the one hand TC’s are notoriously bad except with good glass, but I ‘m starting with L glass. I understand this gives me an f/5.6 prime which is a full stop faster than the 100-400 at f/8. On the other hand, the 100-400 keeps getting accolades at punching above its weight and I bet it has a better digital correction profile since that’s the way lens designs are going.

Use case, just for example, would be the moon or large wildlife (not birding)