But I digress... (not unusual for me.)
The migration you describe is occurring because people are voting with their feet, having found themselves in untenable situations where they lived and now, thanks to the miracles of modern communication, aware of the possibility of going elsewhere.
Many (though not all) of the USA "illegal immigrants" and many of the legal ones apply for permanent residence via asylum laws, citing uncontrolled gang violence in their homeland. Rather than stay there and push their own governments to get rid of the gangs, they just leave and look for a place where the gangs haven't reached yet. (To which I say, good luck with that.)
The large number of refugees from war-torn areas and strict Islamic areas is a flight from (pardon my language) a crap-hole of a territory. There, the gangs call themselves "political warriors" or "jihadists" or some other fiction that substitutes for "violent thug." Again, the refugees don't have any luck in getting protection from their governments and so vote for their feet.
The main difference between the USA influx (mostly Hispanic) and the European influx (lots of Muslims) is that the Hispanic influx would really LIKE to be able to assimilate to the USA, and the only thing they would bring in would be some lively festivals. The Muslims want to remake their new places into another place where a crap-hole can develop because they don't realize that the problem is Islams refusal to consider other Muslims as the source of their trouble. They look outwards to blame the infidels, not inwards to blame their own thuggish cults such as the Wahabbis (or some similar name, and I apologize for not looking it up before posting.)
Is mass migration a net benefit? I am ambiguous on that one. From an altruistic viewpoint, it is good that people can find a better place to live. However, what I fear is that when enough people leave the crap-holes and gang-riddled streets, the thugs won't have enough people to terrorize, rob, and even plunder. At that point, they might try to follow their victims. If that happens, our streets will become crap-holes. In the USA we are allowed to own guns so can resist the thugs for a while. We can shoot back. But other areas are not so lucky. If the influx of people can assimilate, that would be good. If the influx cannot or will not assimilate, I see a disaster.