Considering the sheer size of the two ships, it's fairly safe to assume the Constitution would have a higher power output, which would translate to more weapon power, more shield power and so forth. Not to mention a larger crew which means better damage control. The Miranda would seem to have the edge in maneuverability, which coupled with it's smaller profile and seemingly wider weapons arc would make the contest interesting.
The Constitution was shown to have aft torpedoes in Enterprise's In a Mirror Darkly, so you could make an argument either way if the refit did or didn't, because we didn't see it. Almost every Trek video game features them having an aft torpedo and it's a boneheaded design flaw if it didn't. Even if it did though, most of it's firepower is concentrated towards the sides and bow, and not the rear. I seem to remember a display(in ST3 I think) clearly calling Enterprise a Heavy Cruiser and Krudge's crew did say "Federation battle cruiser" when annoucing Enterprise's approach. So Reliant would seem to be a frigate or light cruiser at that time.
I'd have to give the edge to the Constitution is a straight up fight. Though a Miranda may well be able to evade and escape from one if it isn't forced into battle. Kirk's blame or lack thereof aside, Reliant was more powerful than Enterprise because Khan got in the first hit with shields down and that was the determining factor in each subsequent engagement.