Murder is down in line with the rest of crime. What that tells you is that even crime that's hard to fail to report follows the general trend.

Shooting people and high speed chases are bad tools for apprehending criminals. They are more likely to harm innocent people than criminals. Facing off with "violent and brazen" criminals doesn't change this, but also the fact that crime is down suggests US criminals are in fact, neither more violent nor more brazen than those in areas where police use less destructive methods.