I think the discovery bolts are better then the Kelvin timeline ones. They shoot faster, and seem way more accurate.
The ones in the Kelvin movies just seem to fire wildly at the target.
Also, don’t forget, Wrath of Khan had bolts of some sort as well. Or at the very least just very fast firing beams.
The Defiant's gatling/pulse phasers were a slightly different take on the bolt style.