I hadn't really thought about this consciously, but you're very right, the phasers in TWOK are really quite something. Loud, mean energy bursts. I can hear the Reliant's phasers tearing into the Enterprise right now in my mind with Horner's score marching along in the background
The phasers being more powerful than before (TOS) also fits since we learn in TMP that phaser power is now channeled via the warp drive.
It really is a shame they didn't use them again.
The hand phasers in TWOK are also in that same vein, they disintegrate people pretty brutally, more like what would become a disruptor effect, with again a sound effect that shows it means business.