There seems to be a general understanding that the Reliant was originally "outgunned" by the Enterprise
How so? The outgunning could have been there from the very get-go. Spock's analysis is quite neutral on that.
Khan's own analysis is that his ship after all the damage and subsequent repair is the more powerful one
even when main power remains down, possibly suggesting an inherent advantage. Sure, Khan was fooled into thinking the
Enterprise was in worse condition than she really was, but even then, the actual events of the battle suggest Khan was still right.
Plus Reliant was shown firing phasers from those cylinders on the roll-bars, at least in the forward direction.
More exactly, each cylinder had two single phaser emitter pimples on yellow squares to the
upper sides. The beams came from those, not from the forward spire (which only ever emitted solid white light) or the aft part.
Early audiences got that wrong and the fans thought that these guns were physically bigger than the main guns of the
Enterprise, when in fact they were smaller (single vs. double). So they went for the idea that Khan exclusively fired these guns because they were the most powerful in his arsenal - an assumption that, while quite possibly true, was based on a false premise.
Like
Bry said, we have little idea about the true "caliber" of the guns. It might be unrelated to the physical dimensions. Or then Trek firepower is unrelated to the guns altogether, being solely determined by what the power plant could currently pump out.
Timo Saloniemi