i always though the Miranda was to the Constitution what the Nebula was to the Galaxy, Both share the same technology but Miranda/Nebula are packed into a smaller volume.
I'd say tactically both the Reliant and Enterprise armaments wise were about equal. The deciding factor is hull/armour, In a slugfest between these 2 ships i think it comes down to who can take the most punishment. I'd say in a fair fight the Constitution takes it. But with some major battle damage to the point of being mothballed shortly afterwards.