There's a "WARP PWR" indicator on one of the panels they zoom into, I believe in Sulu's Helm console half, just below a group of four vertical slide-like indicators for "PHASER CHARGING" status. This "WARP PWR" indicator may be related to how much of that PWR is available to weapons - and it does hover around the 1/3 - 1/4 mark. But it does so before Khan has fired a shot!
...OTOH, whenever we see Chekov's station later in the movie, the four "PHASER CHARGING" and the four similar "PHOTON TORPEDOS" slides seem to be up to max. Although happily, we never see them up close at such times where dialogue would demand that just "a few shots" be available. They probably "were" down low during the latter half of the first fight against Khan. But them being up again in the second fight would seem to void the idea that two badly wounded ships are trading weak punches because they can't do anything worse. Rather, we can probably argue that Khan in the nebula fight was wounded and unable to deliver "full kill" phasers, whereas Kirk simply held back because he was the good guy.
Timo Saloniemi