I'm a fan of the right to keep and bear arms. But I prefer unarmed police and restricted gun rights to strong gun rights combined with a police force that regularly shoots civilians 'by accident'.
This is in the context of a discussion that uses the U.S. as an example of a country where cops bear arms as a default and New Zealand as an example of a country where they don't. The danger of police carrying guns is readily apparent given recent events and discussions about them in the U.S.: if they have guns, cops might use them all too often. I'm guessing a comparison of death by cop statistics between New Zealand and the U.S. would support that view.
But there's another important variable: the availability of guns to citizens. Apparently (based on information in the thread I link to above), it is pretty limited in NZ, whereas in some U.S. states, any Tom, Dick and Harry can buy a gun. Let me submit the theory that this is what really counts. I'm basing this view on a third data point: Germany. Here, cops routinely carry guns. If you play your music too loud at 10.01 p.m., the cops you'll find knocking on your door will be carrying fully loaded pistols. And yet, in 2011, police fired only 85 bullets while on duty (presumably not counting training), of which 49 were warning shots and 36 aimed at people; 15 people were injured and 6 killed. The numbers for 2010 were 96, 59, 37, 17 and 7, respectively.
Let me wildly generalize from that small heap of data and assumptions: When the probability is high that the other person has a gun, police will be quick to shoot. Part of this is split-second rational(ish) decision making, but there is also a wider institutional context in which this occurs - such as police guidelines about when to shoot and where to aim. The way to reduce police killings of citizens is hence to make it hard for citizens to bear arms.