A lot of this was covered in a previous "Miranda as combat monster" thread.
There may be differences between the two ship classes beyond visually counting photorp tubes and phaser banks.
If you wanna accept the ships as "heavy cruiser" or "frigate" or "light cruiser", there may be differences.
Sure, you can count the phaser banks and compare numerical superiority. But maybe the Constitution class phasers are an equivalent of a battleship 15" gun while the Miranda class phasers are equivalent to a cruiser's 8" gun.
Maybe the Miranda's torpedo pod carried a smaller less powerful torpedo type than the Constitution class.
Perhaps the deflectors were also different, the Constitution had battleship-like 12" of armor type versus the Miranda 10" of armor type.
And don't even start with the mega-phaser cannon thing...