You've also go to go all the way back to the formation of both police forces.
In the USA, the first police forces in the South were mercenaries hired to bring back runaway slaves, and in the North they were born out of rich industrialists managing to lever their influence to get the local governments to pay for their private security forces.
There was never a Robert Peel character, who proposed a police force which protected civilians by being an alternative to the military which was being used before. The Met was set up based around the
Peelian principles of policing, which is all about being a service to the public, not using force and that the police are members of the public.
So from the very beginning of their existence, the two countries approach to policing is poles apart. One was to hunt down and punish people (slaves) and the other was to prevent crime and get rid of oppressive military policing that existed prior.