This is a fantastic question!

You are correct partially that immigrants from specific regions might be more likely to embrace chassidic life, but immigrants from those same regions often abandoned Jewish life or adopted it in other forms. The real dividing line, instead, ends up being TIME- it was about immigrants who came to the US after WWII.

(Note- most spelling will be based on Hebrew pronunciations rather than Anglicized ones- please let me know if anything isn't clear.)

Now, there were chassidic Jews and even a couple of chassidic rebbes (leaders of chassidic groups) in New York prior to WWII, but as I noted in this past answer, there were very few, and no real communities that built up. Part of the reason is that many of the most devout Jews, the ones who would be most likely to listen to the words of their rabbinic leaders, did not go to the US because it was seen as a treifene medina (an impure country) where Jewish tradition was lost; staying poor and devout in Poland or Hungary was seen as better than being rich and secular in New York. And indeed, as you note there was a high assimilation rate among the Jewish immigrants to New York, especially in the second generation. Those Orthodox Jews who did emigrate to the United States simply assumed that there was no possible way to replicate the kind of Jewish life that existed in eastern Europe in their new homes in New York (or other cities, though those generally ended up following New York's lead, as nearly all American Jews started off there even if only briefly).

But another part of the reason is that the rebbes of the major chassidic groups were back in Europe. Pre-WWII, adherence to a specific chassidic leader could be more fluid than it is today, when you can see multiple chassidic groups, each with their own rigidly divided community institutions, in the space of a few blocks in some areas of Brooklyn; adherence was often at least partially geographic in basis, and someone who moved, even if they retained reverence for the rebbe from their place of birth, may end up also adhering to the rebbe of the new place. So if a chassid were to choose to move to the US, he would be leaving his rebbe and his court behind, even if he still revered the rebbe on his own. There were a few rebbes who set up shop in the US, such as the Boyaner Rebbe in Manhattan and the Malach in Brooklyn/the Bronx (about whom more in a minute), but their very small chassidic groups did not quite resemble chassidim as you would picture them today. (Anecdotally, my great-grandfather came to the US from Poland, where he had been a chassid of a particular chassidic group, and then briefly became a chassid of the Boyaner Rebbe in New York. Because he ended up not finding the worship there satisfying, he ended up retaining his Orthodoxy but losing the specifically chassidic part of his identity.)

That said, by, say, the 1920s in the US- about when Jewish emigration to the US dramatically slowed to a trickle due to severe immigration restrictions- Orthodox Jewry in the US weren't divided by chassidic or non-chassidic- it was more about traditionalism vs modernity. While traditionalism had always been a force, it generally was one that died out in the second generation; most of the successful Orthodox organizations, such as the Orthodox Union and Young Israel, were ones that made an effort to reach out to secularizing children of immigrants and create a religious experience that combined religious observance with full. purposeful participation in the American dream. It was in the 1920s that a really significant force of stalwart traditionalists made their impact. They mostly lived in Brooklyn, mainly in Williamsburg (right across the bridge from where they started off, the Lower East Side of Manhattan), and slowly began to establish their own educational institutions specifically targeted at students (initially mainly boys, though a school for girls eventually started as well) who wanted a completely traditionally-minded education. Whether such traditionalists came from backgrounds which were chassidic or not, they were united in a specific outlook that instead separated them from the avowedly Modern Orthodox (as they came to be called), with their emphasis on higher secular education and, often, coeducation (which traditionalists did not believe in). However, even as these divides were being set on an institutional level, as a general rule the Orthodox community featured a lot of crossover between sides on an institutional level.

One interesting exception was the Malachim, and in a sense their tiny fringe movement presaged the greater chassidic movement to come, and the split that would come between chassidic and non-chassidic traditionalists. The Malachim (literally, angels) were followers of a Bronx rabbi named Chaim Avraham Dov Ber Levine (who was called the Malach, or the Angel, by his followers), and he preached a movement of chassidic asceticism on the lines of what they had experienced back in eastern Europe (or even more so, as a shield against the impurity of America). This asceticism ranged from wearing the distinctive peyos (sidecurls) and beards to speaking only Yiddish to consuming no secular media (such as newspapers and films); even some of the most diehard traditionalists previously had capitulated on at least some of these items, conceding that they had to integrate somewhat with the dominant culture in order to maintain what traditions they could. Specifically, Rabbi Shraga Feivel Mendlowitz, head of Torah Vodaath- one of the first of these traditionalist schools in Brooklyn, where students learned Torah and Talmud all day and then did a high school curriculum at a public night school- had made certain concessions but then, in his admiration for the principles for which the Malach stood, he held the Malach up as a saintly rabbi, only to then expel his disciples from the school in the 1930s when he became concerned that if the Malachim were too influential, the school's asceticism and chassidic tendencies would alienate the rest of his student body. In other words, while traditionalism was valued, it was assumed that in the comparatively libertine US, it could by definition only go so far. Upon their expulsion from Torah Vodaath, the Malachim established their own school, Nesivos Olam, and began to specifically marry amongst themselves, shrinking back from the rest of the Orthodox world.

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