Hi there,

This question is asking about millions of people over the course of a century, so it's hard to give you a quick answer. The first step towards answering it, I think, is to lay out how potential immigrants formed their conceptions of the United States. No one (or at least no one past childhood) came to the United States without any understanding of conditions there. There were emigrant guidebooks, as well as publications in periodical form that tried to inform potential migrants about the opportunities and pitfalls of migration. Walter Kamphoefner notes that these were likely not very effective, however, and at any rate it's hard to determine how widely they circulated or how seriously they were taken.^(1) We should also note that while the stereotype of these publications is of reckless promotion, transatlantic print materials were as likely to pump the brakes as they were to spur potential migrants on. A good example of this is a periodical called Transatlantische Studien, which was written by several German immigrants/refugees, and sought to dispel any overly-romantic visions potential migrants might have of the United States.

But most information came back to Europe in the form of letters from friends and relative who had previously gone to America, or from acquaintances who returned to Europe themselves (side note- I've encountered a common misconception among many people that today's migration to the US is substantially different than that of earlier generations because immigrants back then came with the intention of permanently settling in the US. There's no reason to believe that's due to anything other than transport being more difficult in the 19th century, and at any rate Mark Wyman estimates that 1/4 to 1/3 of European immigrants between 1880 and 1930 returned to Europe permanently. This is significant because it means a very large portion of immigrants to the US would have had direct contact with multiple remigrants).^(2)

I'll quote from a letter of German immigrant Johann Bauer, who lived in Missouri in 1868, so we can explore this dynamic further:

"I don't feel the least bit hurt that [my brother Friedrich] didn't visit me, although I had dearly wished it; on the contrary, I can’t help but smiling that he got so terribly homesick & left America in such a hurry, bitterly disappointed that it’s not possible to make a fortune here in one year. America only has a few great advantages that you don’t have in Germany, the greatest is that you can be more independent than there, that you can start something today, & if you’re not happy or satisfied you can start something else tomorrow & without making a stir. That is the main thing that makes America so dear to people, the freedom of movement, in many other things Germany is almost as good. If Friedrich had come to see me, I could have given him some useful advice... Finally, I prophesize to you that Friedrich will come back to America. America, with all its adversities, has a power of attraction like no other country, because here you can take up whatever you want. It is a great mistake to think, like Friedrich does, that you don’t have to ask anyone for anything, he can be convinced of this later."^(3)

Bauer tells us several interesting things in this passage:

• Friedrich deserves little sympathy, because he should have already known that the US, though in many ways superior to Germany, was not a magical land of opportunity
• He reiterates that point to his remaining relatives in Germany, which should then presumably inform any other potential migrants' decisions to emigrate
• He points out that Germany (as a region and not yet as a country) has points in its favor as well
• He assumes Friedrich's ability to go back and forth between the US and Europe
• He notes that America is as powerful as an idea than as a reality for many immigrants

So where does this leave us relative to your initial question? The "better fortune and living conditions they expected" all depended upon, well, their expectations. Transatlantic immigration discourse was primarily dedicated to managing those expectations. In my personal experience of reading through countless letters from German and Irish immigrants (primarily from the Deutsche Auswandererbriefesammlung of the University of Erfurt, the Irish Emigration Database, and several edited volumes), the emphasis was on setting realistic expectations so that hopes would not be dashed by encountering struggles in America. Many immigrants got the message and came to the US clear-eyed. But we know that many, like Friedrich, did not heed those warnings and were bitterly disappointed. We also know that there were people who bragged about their experience in the US, often to the point of exaggeration. But other immigrants actively tried to correct their misrepresentations; for example, one German immigrant warned in 1884 that “Two fellows from Oberhausen are coming home, named Heinrich Eng and another one named Haas, neither of them were in the country for very long, but they’re both a couple of liars and braggarts. They don’t know anything about work here. The few months Haas was here, he had the best job, in the pillar, and now he boasts that no one has to work hard over here, but we work harder and longer than anyone at home.”^(4)

Who won out in this messaging battle? Circumstantial evidence would suggest that the pragmatic ones did. Increased immigration tracked extremely closely with economic upticks, and lulls with depressions and recessions. That suggests that immigrants were well-positioned to seize economic opportunity while avoiding dislocation and uncertainty. Even among the worst-off immigrants in the United States, such as the Irish in Five Points, their position in the United States usually reflected a relative improvement in their material conditions.^(5) Obviously some portion of immigrants found conditions worse than they had hoped, but insofar as the first step in migration - obtaining information about America - was dominated by an exercise in managing expectations, that portion was kept as low as possible.

​

1 Walter Kamphoefner, The Westfalians: From Germany to Missouri (Princeton: Princeton University Press, 1987), 57-58.

2 Mark Wyman, Round Trip to America: The Immigrants Return to Europe, 1880-1930 (Ithaca: Cornell University Press, 1993)

3 Johann Bauer to parents, friends, brothers, and sisters, Willmothville, Adair Co, MO, 4/11/68, quoted in Walter D. Kamphoefner, Wolfgang Helbich, and Ulrike Sommer, eds., and Susan Carter Vogel, trans. News From the Land of Freedom: German Immigrants Write Home (Ithaca: Cornell University Press, 1991), 164-165.

4 Matthias Dorgathen to parents and brothers, Buckingham, OH, 9/28/84, quoted in Walter D. Kamphoefner, Wolfgang Helbich, and Ulrike Sommer, eds., and Susan Carter Vogel, trans. News From the Land of Freedom: German Immigrants Write Home (Ithaca: Cornell University Press, 1991), 461.

5 Tyler Anbinder, Five Points: The 19th-Century New York City Neighborhood that Invented Tap Dance, Stole Elections, and Became the World's Most Notorious Slum (New York: Free Press, 2001), 42-66.