I lived in Houston for about twenty years. I remember once reading an article in the Chronicle about how it was that civilians had a higher kill rate in gun fights with perps than the police.
From what I have read, citizens have a better record of hitting the opponent and not hitting unintended people.
I believe that there are three primary reasons for this, which have little to do with the skill of the shooter:
Citizen defenders have the trouble come to them, they do not usually go to the trouble, as is most commonly the case with police. Thus they have no difficulty in knowing who the bad guy is. Police often have to figure out who the bad guy is.
Citizen defenders are usually not in crowded areas. Most criminals wish to avoid crowded areas when picking a place for a crime.
Citizen defenders are often on their home turf and know the area well, very often in their own home or store. This is seldom the case in police shootings.
All of the above combine in such a way that police miss more often and shoot the wrong person much more often than citizen defenders.