The Michelins have thinner sidewalls than the Bridgestones, so they typically need a little pressure.
As to what pressure to run. Depends on road surface, weather, temp, and mostly importantly what pace(how fast) you are riding.
Generally;
40-42psi for commuting COLD
35-38psi for twisties COLD
29-35psi for trackdays COLD
Tire pressure is not something you set once and its good for everything. Tire pressure needs to be adjusted depending on what you're doing, the road you're doing it on, and temp...