I'd submit that police have an advantage over their suspect and us in a few ways.
1) Police almost always outnumber their suspects.
2) Police rarely are in an encounter where backup is not on it's way. Hell I can't even get pulled over by a single police car anymore.
3) Police are actually using their skills "in real life" everyday. If all you did was fight on the street you would probably be a better fighter then 90% of the worlds martial artists.
4) In addition to their police training and constant application of fighting in real life, many police also can choose to get martial arts training. For example, there are many officers in my bjj club who comment often how bjj has improved their ability to control suspects.
Oh yea, and I forgot
5) Police have stun guns, firearms, clubs, handcuffs, and other objects of control.