I don't see what that's relevant. If the UK police respond to reports of a person with a gun without being armed themselves that's clearly braver that American police who respond to literally any report with enough military hardware as if they fear for their lives.
Because the likelihood of a police officer getting shot by a criminal is far higher. Not just in domestic violence situations, but also in everyday policing. An example: here in Germany even if you push hundreds of kg of cocaine you'll get six to eight years behind bars. Not worth shooting a police officer at a traffic stop over it.
In the US? Decades behind bars at least, life if you're in a "three strikes" jurisdiction - that's a massive incentive to shoot the cop and attempt to escape when you got nothing to lose anyway.
Not just fewer, a couple of orders of magnitude fewer guns (maybe more). Also a populous with more mental care for those who are in dangerous mental states.
With this logic: The US police is way braver, they have to be adrenaline fueled jackasses to dare do their job of killing citizens.
With normal logic: If not everyone is at the mercy of eachother not popping heads for lolz we don't need to arm the police as heavily, and we can hire people that are good at deescalation rather than shooting back.
Bit of a smug take coming from a place with fewer guns than people.