If you just shoot them, one hit on the shields is enough, you will get a 100Cr Bounty (note that it's not a Fine) and commit one crime. If you then continue until you kill them you will get a further Bounty of 5k(?), gain notoriety and commit a second crime. For BGS purposes it's counting the number of crimes committed.
On that basis, even though you get two crimes if you destroy them, it can be quicker to just tag each target once for the initial Bounty and move on with no notoriety to deal with.