I always wondered why Neri started opening fire when he did instead of letting Barzini get closer. I think this could be chalked up to another "artistic license" where FFC wanted Barzini's death to be dramatic.
That entire scene was shot through (no pun intended) with "artistic license." Note how Neri whacks three guys with a mere six-shot, police issue .38 Special, a gun not noted for long distance stopping power, while Rocco and an associate use a pair of Madsen submachineguns to kill Tattaglia and his
putain from a distance less than ten feet. And why did poor Clemenza have to haul his considerable bulk up many flights of stairs, lugging a full-barrel-length shotgun, to whack Stracci in an elevator?