I don't think the difference is European in nature, I think that immigrants 100 years ago have a totally different experience than today.
I can only speak to my family's history and that I saw growing up, but my great-grandfather was an immigrant from a Slavic region (to be technical, Poland didn't exist yet, but he was a Catholic who spoke Polish).
To make a long story short, none of his kids ever spoke Polish. That wasn't familial pressure, but the physical and emotional abuse inflicted on children in schools to beat the slav out of them if they acted or sounded "fresh off the boat" - to the point where four generations later, all of us know that phrase because it's been said to us one way or another.
Contrast this with the most recent wave of Polish immigration to the same neighborhoods almost 80 years later. These are kids I grew up with. They had Polish clubs in school, they went to "Polish school," they spoke the language fluently and publicly, and to a certain degree that was celebrated by the rest of the community. The external pressure not to be Polish is essentially gone.
I don't have a grand point here, it's just something I think about a lot in these debates. I learned what the experience of my ancestors was, and saw something of what happened to my peers, and the only difference was 100 years. It seems to me the difference between what we think of as assimilation is really how likely a community is to join the melting pot depending on the internal or external pressures on that community.
Yeah, fast changing demographics means fast changing values.People that come in mass from failing or disfunctional or just very different societies can and do bring with them "incompatible" values. Us modern ability to integrate / assimilate people in mass is probably ovverated, expecially in a fast paced mass migration scenario of a multiethnic society. the future is probably some version of Brazil
Usa got lucky integrating most europeans first and skilled immigrants later. but it struggled with other demographics, notably afro-americans, native americans