The Miranda's not really lighter than the Constitution, though.
But the definition of "light cruiser" ITRW had basically zip to do with displacement anyway. It was solely a matter of gun caliber, and many a light cruiser far out-bulked contemporary heavies, or (in Japan and the US) was eventually changed into a heavy cruiser simply by swapping her triple 6in turrets for twin 8in ones.
Anyway, I don't remember where I read this, but the Reliant in TWOK was meant to be more advanced.
The original story concept was for Khan to capture an outdated starship - a TOS Constitution
... And then (initially) triumph simply because he was the better or at least more ruthless captain.
Again, from TWOK, the weapons and hulls seem evenly matched. Of course we don't have much to go by.
Or, we have a lot to go by (basically more than in any other TOS episode or movie), but both the hero and the villain are either pulling their punches or fighting wounded in all
the witnessed exchanges of fire.
If we assume identical phasers and torpedoes for both, then the battle is probably decided on one of two things:
a) Some things in TOS suggest that first hits count, much like in early 20th century naval gun battles, so the ship with better long range sensors should win.
b) Some things support 17th-18th century naval gun battle models instead, where the ability to endure long pummeling is decisive, so the ship with better shields should win.
Apart from that, I'm not sure what real advantage the aft torpedoes of the Miranda
would give, except perhaps in chase battles.