A lot of Italians definitely went to both places!

I don't know a lot about Argentinian history, but I do know a good deal about this period of immigration from the American perspective.

If you were emigrating to America from Italy, the answer is mostly yes, with some exceptions. Most Ialians either settled in the cities of the Northeast, stretching from Boston to Providence to NYC. If you emigrated there, you would have a life of service work or factory work ahead of you, and you would live in tenement-type situations. You would be viewed with some suspicion for being Catholic, but in those cities you could certainly do better than your Southern Italian contemporaries who never left home.

The other major route of emigration followed the citrus trade into the south, primarily through Louisiana/New Orleans. This wasn't as great of a place to end up, for a lot of reasons. There /were/ more Catholics down there, so you have that going for you, but otherwise...Italians were not viewed as white. The white bosses of Lousiana didn't mind hiring Italians because they would work cheap, but they considered them barely a step above black people. You'd have to deal with a lot of "they took our jobs", especially if you got into more high paying dockwork, or you would be making slightly better than sharecropper wages on a big farm.

The White League (think more "classy" KKK) helped whip up this distrust and hatred (Italians were often viewed as criminal in nature and willing to murder casually over perceived slights) until in 1891 11 Italians were lynched at once after being acquitted of murdering the New Orleans chief of police.

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On the other hand, if you were able to hang on through this period, Italians would slowly become accecpted as "close enough to white" for Louisiana. If you hung on into the early 1900s, for example, you could open a spaghetti restaurant - spaghetti dinners start getting advertised as a fancy, exotic meal in the Times-Picayune around then. You coulda also gotten in on the ground floor of Progresso, or founded a similar company capitalizing on this desire for Italain cuisine.

And, if you hung on another decade after that, you'd be instrumental in helping start the creation of Jazz through introducing your black neighbors, who you would have likely hung out with for solidarity reasons, to some of the wind and horn instruments that became essential to the genre.

All that being said, I think I would suggest Argentina over America in this time period, unless you land in one of the bigger east coast cities.

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Sources:

Deep Water: Joseph P. Macrea and the birth of the American Mafia by Thomas Hunt and Martha Macrea Sheldon

The Italian American Contribution to Jazz by Julia Volpalleto Nakamura

The Lives of Undistinguished Americans as Told by Themselves by Hamilton Holt

Vendetta: The True Story of the Largest Lynching in U.S. History. by Richard Gambino