You Europeans have no value of life.
Most Europeans countries allow for the use of deadly force when defending one's life, much like the US. However, what isn't tolerated is the killing of somebody fleeing a crime scene. That means that Europeans actually value like more than Americans.
Should I bring into light the Crusades, persecution of the Jews [and no not just Hitler], rape and pillage of villages during feudal days. Great Britain taking everything within sight, the Zulu wars.
And yet everybody in Europe loves saying the US is a bunch of war mongers, but they choose to ignore their own bloody past to make themselves seem like they are "higher" on the moral ground.
The difference is that for most European countries those crimes are in the past and have long since been apologised for. The United States, on the other hand, hasn't apologised for the use of nuclear weapons against civilians in Japan, for supporting coups in Iran, Guatemala, Brazil or Argentina (amongst many others), for the chemical weapons used in Vietnam or Iraq, for the targeting of civilians in drone strikes, for undermining democracy in Palestine and Egypt, for the torture of prisoners, etc. In fact the US keeps racking up the war crimes.
So yes, Europe does hold the moral high ground. In fact the EU received the Nobel Peace Prize in 2012, though the award doesn't have as much credibility since it was awarded to Obama in 2009. But that doesn't mean the EU is faultless, as both France and the UK supported an attack on the Assad regime without UN support. And many European countries have opposed diplomatic efforts by Palestine and ignored the war crimes being committed by Israel.