The Phasers in Star Trek II: The Wrath of Khan were cool, but man! It's a great thing Kirk is a better marksman than Khan allegedly was. If I were Chekov, I'd be mighty nervous having Kirk blasting that thing right at my ear.
The bubble shields were originally invented as a cheap way to depict weapon impacts. As CGI technology moved forward, they were able to show the more visceral bubble-free weapon impacts of DS9's later seasons, where ship hulls were shredded. It doesn't make much sense in-universe, but it certainly looks cooler.
I would think that having "Pulse Phasers" would allow the phaser array to recharge quicker, but would lack the punch needed to take down a capital ship (but are good against smaller ships and objects), whereas standard Phasers would have a stronger punch against a capital ship, but the recharge would take longer.
There was an idea floated about that what makes a phaser particularly effective is how long it stays in contact with a ship's shield--the longer the phaser contact, the more it wears down the shield. Pulse phasers would seem to operate on the same principle, but makes it harder for a shield to disperse (or deflect) the energy from each rapid-fire hit.
Even those pulsed a bit. The streams were steady, but each bean seemed to alternate in brightness IIRC
Perhaps in addition, I've read somewhere that the phaser beam's most effective strike is the initial contact between beam and shield. A dozen pulse phaser shots, however, mean a dozen effective strikes. But with that said, we've seen instances where prolonged, sustained phaser beam blasts do indeed inflict quite a lot of damage. One of my favorite shots in all of Trek is a Cardassian Galor getting shoved to the side by the concussive force of a few phaser blasts from two Galaxies.