Of course there are serious issues of culture and individual responsibility separating these groups, but nevertheless, unless these immigrants are from highly violent or authoritarian places, this is almost never true. Most immigrants to this country coming from Asia, for example, have no clue that their struggles and obstacles simply don't measure up to those of Black people already living here.
Black people are the primary targets of the police-prison continuum in this country, as the percentages prove. Let's also remember that the US police-prison system is massive. We currently have more people imprisoned than any country in the history of the world- the combined incarcerated populations of the Stalinist Soviet Union at the height of the Gulag period and Maoist China at its peak still can't match up to the number of people imprisoned in the US now, and the largest demographic among those imprisoned are the Black poor. The percentage of incarcerated Americans is only growing, too, meaning that this system is actively growing despite crime rates remaining stable, so it's not as simple as saying that these people are getting themselves caught up in it by their own actions. In at least one sense, the "system" is indeed out to get them.
Furthermore, Black people's quality of life and mortality indicators are often comparable to those of wartorn, sub-Saharan African countries. Check the HIV rate in poor, heavily-Black areas, like the South Bronx, for example... it's worse than most poor countries in Africa who have HIV epidemics. On the whole, Black children face conditions that most immigrants do not, despite coming from the "global South" or "third world."
The truth of Black life is invisible to most people, including most of those who interact with Black people on a regular basis. Personally, I hear fewer Black people shytting on immigrants, than I hear European, Asian and non-Black, Hispanic, and even some privileged African immigrants shytting on American Blacks on a regular basis and asking why they just can't do what the immigrants do. I'm not suggesting we give people a pass for negative, self-defeating, or destructive behavior, of course. The point is that the conditions faced by the Black population are unique and cannot simply be analogized to those of immigrants, especially in a way that makes them seem easier.