There are some significant differences that result directly from our changed immigration laws.
Previous waves of immigration (prior to WWII) involved people from all walks of life because there were really no immigration laws in America. So you got Italians and Irishmen (for example) from a relatively broad spectrum of society.
Modern immigrants must fit much narrower, stratified classifications. They tend to either be unusually high-status (well-educated, rich) or unusually low-status (refugees or illegal). It is extraordinarily difficult for a middle-of-the-road immigrant to get here and do middle or lower-middle class work–they can really only come as family members of people already here. So especially for new immigrant groups from post-1970 waves, there is a very stratified class. Arab-Americans are a good example. Generally speaking, first generation immigrants from the Arab world tend to be either engineers or struggling part-time employees. And that’s a policy choice we make, because they only get here by having a high-status job or as a refugee.
Of course, the fact that immigration is exponentially more difficult in 2016, unlike 1916, means that more of the immigrants are illegal. And illegal immigrants have a much more difficult time integrating, among other difference that are obvious from the fact of them being always in danger of deportation.