The ship phasers used most in nuTrek seem to be some variation of the pulse cannon type phasers on the Defiant in DS9...
But I think they have the cutting-beam type too, we just don't see them as often, unfortunately.
On the Kelvin at least, the classic TMP-style dual mount phasers still fire in beams. The pulse phasers on that ship seem to be a sort of additional CIWS (close-in weapon system) like the Phalanx on modern ships. Rapid-fire last line of defense anti-missile phasers.
The problem with this is Kelvin's pulse weapons were never used to shoot down Nero's missiles and appear to be aimed at the Narada itself. They are, accordingly, more likely to be some kind of quick-firing multi-turbe torpedo launcher in an anti-ship role (with possibly smaller-than-average torpedoes).