This is true. It in fact feels to me that I need more pressure on my diaphragm when playing the Soprano than when playing the tenor. I haven't blown it for about 3 days and tonight trying out a new more open mpc with reeds slightly too hard for it I found my diaphragm hurting me just below my ribs after what was barely any time. That never happens on Tenor no matter how many days off I have. I see it as a combination of these things: the greater resistance of the narrower bore + the larger tip + the slightly harder reed = greater blowing pressure on my diaphragm. On top of that, I probably didn't have a loose enough embouchure due to those factors and the greater pressure on the reed made the bore at the entrance of the airstream even tighter. This causes back pressure in the same way that trying to force water at high pressure through a narrower pipe actually blocks the flow. I believe that there is actually a limit on how many cubic liters of liquid or air can pass through a pipe at maximum pressure depending on its diameter. Is that correct, and if so I don't know the exact term for it but Dr. G proablay does. Maybe that's the venturi effect, or is that something else?I believe the formula for this is speed=Pressure/resistance
The smaller the 'pipe' the greater the resistance, thus you must increase the pressure to get the same airspeed.
It's actually more complicated, but this is the basic model.