I've run 28 (Panaracer Ribmo) & currently 32 (Panaracer Pasela TG) on one commuter and 40 (Michelin City) on another. (On my "road" bike it's Continental GP4000s 25c with 90 front/100 rear.)

Personally the biggest benefit I've found is the ability to run lower tire pressures in wider tires. With the 32c it's 60psi front/70psi rear and with the 40c it's 40psi front & 50psi rear.

Personally going from 23 to say, 28 you will notice a difference, but make sure to experiment with tire pressure.