The more cooperative relationship in Europe was the result of the labour movement largely
winning, in the sense of gaining sufficient political power that the balance of legal protections shifted to a point where the struggles even when heated are generally much less of an existential crisis.
Keep in mind that for many decades, especially from the 1840's onwards, much of Europe was a total powder-key with countries facing revolutions left right and centre, and the political landscape changing rapidly to accommodate this. E.g. Bismarcks massive healthcare and pension reforms in the 1880's were inexorably linked to his fear of revolution. To take another example, in 1923 the Norwegian right wing were absolutely horrified when - after they failed to negotiate a coalition - the king appointed the Labour Party leader to the post of prime minister (at the time Labour was still a communist party); the government was voted down immediately (and the king would have known that would happen), but it still forced the other parties to realise they could not ignore the demands of the labour movement any more.
In the post-war periods the social democratic and socialist parties across Western Europe either got into power or became a substantial threat to the right in most countries, and as a result you saw sweeping welfare reforms, healthcare reforms and others across large parts of the continent.
Unions that had for decades in many cases been outright communists were moderated by the combination of starting to fear the Soviets coupled with major wins for labour rights that made them less inclined to rock the boat.
It's a whole lot easier to win support for a more cooperative approach when people saw negotiation actually working for them, and employer increasingly being willing to sit down from the start rather than employ the kind of tactics Amazon has been accused of using (I'm not taking a stance on whether or not they've done the things they've been accused of, but these kinds of things are not new in terms of US employers fighting unionisation).
US unions have remained far more militant because US employers have remained far more militant. Active use of actual violence on both sides remained prevalent much longer, for starters.
You're not going to see those hostile fronts change unless workers rights are substantially strengthened to the point that not enough people find the hardline approach worthwhile any more.