While I have nothing substantial to back me up (apart from the fact that the Mac mini's case can house a larger fan), my guess is that the Mac mini will have better sustained performance.
Also, my guess is that the M1 Mac mini's fan's acoustics will be less annoying than the MacBook Pro's fan.
With its thin profile, the MacBook Pro will have a smaller, narrower fan which would need to run at a higher speed to move the same amount of air (CFM) than a desktop system like the Mac mini which can support a larger fan running at a lower RPM.
This isn't Mac specific.
This is the same with Windows desktop PC fans, bathroom fans, kitchen range ventilation fans, etc. To knock down noise, a big fan running at a slow speed is quieter than a small fan running at a fast speed.