You know what's interesting? Both the Defiant and the TMP Enterprise had their phasers fed directly by the warp core, and both (+ the Reliant, maybe all TMP era ships) had pulse phasers (or "pulse-ish" in the case of the TMP ships).
Although we didn't see the Enterprise fire her phasers in TMP and by TWOK they were different again. But as I said, maybe the charging function was added again as a backup.
EDIT: Or, the TMP phasers were an experiment to increase their power output that didn't work well (maybe because it was still too dangerous to have high energy warp plasma circulate though the whole ship), so by TWOK, the ships were outfitted with the old TOS energy distribution network again and the "pulse phasers" were developed, which utilized the old TOS charging mechanism again but were stronger because the pulsed discharge dealt additional explosive damage to the target.
By DS9 then, on the Defiant, the direct warp energy supply to the phasers worked and was also combined with the stronger pulse phasers.
I think the TMP phaser experiment failing is a pretty good one. As for "pulse"-ish phasers as in burst fire weapons rather than continual beams, I'm not so sure on this one. Yes, we see phasers being able to do weird things like "proximity" bursts in TOS, along with the pew pew pew phasers in TWOK, but do we really see much phaser use after that? It seems like the primary weapons used in movie ships turns into torpedoes afterwards.
For the Defiant
phasers, I think the assumption is more that they're meant to be difficult to shrug off with shield modulation. We saw in "Q, Who" that the array phasers could eat HUGE chunks (like 3-4 GCS worth of material) out of the Borg Cube, but once the Borg adapted the phasers didn't do much. So I'd imagine the priority for Starfleet would be phasers that can punch through (in whatever way) of Borg shielding. Like in FC, Defiant
's phasers don't do a lot of damage, but they seem to consistently be punching through the cube's shields.