I've only done one similar comparison – between the Schneider 120mm and Mamiya 120mm Macro.
The Schneider was on an Alpa STC and the Mamiya on a DF camera, both with the new IQ180.
I had the Schneider focused on infinity (a subject with fine detail about 3km away) because I was shimming the back on the IQ180. The air was exceptionally clear that day.
The only exactly matching focal length that I have between the two is the Macro, so I threw it on the tripod, just for fun.
What I found is that wide open the Schneider was slightly sharper than the Macro when it was stopped down 2 stops.
With both lenses stopped to their optimum apertures the Schneider was clearly resolving more detail.
BUT... this was at the 100% on-screen pixel peeping level. Real world, even in really (large prints) I doubt that you'd see much difference except with a loupe.
Anecdotally – I find that in almost all cases good technique trumps small difference in optical quality. Solid tripod, cable release (or self timer at more than 5 seconds), mirror lockup, critical focusing, etc, etc.
Michael