How was the wave of u. s. immigration in the late 1800s diffrent from the previous wave of immigration in the mid 1800s

Hmm, so just to clarify, the 1st wave was in the mid-1800s and composed mainly of Irish (escaping the potato famine) and Germans (coming to America for better opportunity.) The 2nd wave went on from the late 1800s into the early 1900s and composed of people from Eastern and Southern Europe & Asia. 
 
differences-the first wave was mainly from Western Europe, most of these people spoke English, and were able to assimilate (blend in) with Americans; the second wave had very different languages and did not know English; the Italians and Chinese were the two groups of people who did not come to America to settle permanently, but to make some $ and go back ; also, the treatment of immigrants was not always equal > during the first wave, the Irish were highly discriminated against  signs on a lot of windows; * the Irish/Chinese are famous for having provided the labor for building the transcontinental railroad, which was very dangerous!) while the 2nd wave immigrants had it tougher than the 1st wave (because they were more different to the Americans) one could say in general, the Asians had it the worst ] while European immigrants could at least get by with their looks the Asian immigrants were clearly different, and prejudice was a factor from the beginning. 

oh and the second wave also had one extra difficulty  since the poor were multiplying (and most immigrants were poor) it's generalized that immigrants made a large part of the slums

All in all, life as an immigrant was TOUGH! hope that gives you an idea of what our ancestors had to endure in order to give their kids a better life filled with opportunity - aka the American Dream.