If the Miranda-class has an identical power supply, she is indeed superior in battle. She has a tighter shield envelope and those roll bar phasers look a lot beefier. That might be why the Mirandas were in service in the 24th century while the Constitutions were long gone.
I don't think that the Constitution
class is necessarily out of service in the 24th century, but I do think it is possible that members of the newer, more compact and rollbar-sporting Miranda
class might be slightly superior combatants, or at worst equal. I doubt they have quite the warp performance of the Constitution
ships because of the engine placement, but as a frontline starship I doubt her reactor is any less capable; she lacks a dedicated navigational deflector, which might have some protective value for the Constitution
; she probably doesn't carry as many torpedoes.