Someone pointed out years ago, when the debate of just what those Phasers on the Miranda are was raging back then, (It's always amusing when the same debates are had repeatedly) that if you removed the Phaser Banks from the Constitution's or the Miranda's Saucer, they would match exactly the dimensions of the "Mega-Phaser" mounts on the roll-bar.
The Miranda IS better armed than the Constitution. But not by much. The Miranda and the Constitution have the same number of saucer Phasers pointing in the same directions. The Miranda has the two "Roll Bar" Phasers that fire forward and back, for a total of 4 more phasers. The Constitution has those 4 phasers mounted on the Ventral side of the Engineering hull, presumably covering 360 degrees of the Ventral Arc. The Miranda has two forward torpedo tubes, and two aft torpedo tubes, while the Constitution only has 2 forward tubes. Now, a question remains as to whether the Miranda could fire the forward and aft tubes simultaneously, I would say no, but the versatility of being able to fire torpedoes behind you, which the Constitution, lacks gives it an edge in that category. Also the Constitution has 2 Phaser Banks covering the rear arc (above the shuttle bay) which I do not see any similar mounts on the Miranda. (understandable, the roll bar covers that arc nicely) Based on armament, even though the extra versatility of the aft firing torpedoes helps, I can't justify calling the Miranda a Battle Cruiser. Medium or Heavy Cruiser is what I would say it's initial designation was. There is also a question of how durable the ship is, while it's hard to determine from TWOK, it does seem that the Enterprise was able to take more damage than the Reliant was. If it is indeed less durable than the Constitution, then the Miranda has to be designated a Medium Cruiser, it certainly cannot be designated a Battle Cruiser.