I always took the machine gunning of Don Tataglia as payback for the similar over-kill of Sonny. His body would be shredded
While Barzini was involved in the set-up, Tataglia probably did the shooting if for no other reason than to avenge his son Bruno, he certainly doesn't deny it at the Commission sit down.
Neri has to use the S&W Police.38 to pull the whole Police Officer scam - but still that's not much of a margin for error, what if Barzini had a second body guard, or the chauffer didn't go down on the first shot?
Felt Clemenza's choice of a shotgun was a tip to the old country, where the cutdown doublebarrel was the mafia weapon of choice