The migration in the United States in the mid 19th century and the migrations in the present have some similarities and differences.
The Irish immigrants that flooded the United States, migrated because of the potato famine in their country, so people were literary starving and on the verge of existence. The similarity with today's migrations can be see in the massiveness of the migration, especially in Europe, where millions of people are coming from Africa and the Middle East, and it causes big problems.
On the other hand, the Irish had a similar background, and shared pretty much the same values, and the culture and religion were very close with the people in the United States, so the integration into the society was not a problem at all, and everything went smoothly. In Europe, the new migrants are coming from totally different cultural backgrounds, have different values and religion, and languages that are not similar to the one in the hist country. They do not even want to integrate (not all, but the biggest portion of them), and instead of integrating they are actually separating and creating zones where only migrants live and continue to live in the way they did before the migration, and that is causing a big problem. That is a big difference with the Irish migration.