Higher c rating is more power.  Would a 3000mah 3s pack with a 45c have a shorter run time than the same pack with lower c?

No.  C rating has nothing to do with run time.  C ratings has to do with how much current you can pull from the pack without over heating the pack.  Typically this has to do with the internal resistance of the pack.  In practices if you are running a setup that is not RPM regulated you are effectively running wide open throttle.  A pack with the higher C rating would have less internal voltage loss and therefore would place more voltage across the motor.  The higher voltage would cause higher current creating less run time.  Of course the airplane would be flying faster because the motor would be putting out more power because of the higher voltage.   In practice unless their is a huge difference in C rating one would not notice the differance in run time.   Also with modern timers and ESCs run time is set by the timer and has nothing to do with C ratings.   The major factor that determines run time is battery packs capacity rating expressed as MAH.  A 1000 MAH battery would have twice the run time of a 500 MAH battery.