That's just the point - they were waves - as in a one time shot. After a few generations, with no ongoing support, they assimilated and became Americans. Most of them wanted to anyways.
The current situation is not a wave but an ongoing and increasing flood. Instead of ghettos forming for a generation or two and then dissolving, they now get constant reinforcements and harden into Third World barrios. The fact that our government panders to them with native language ballots, etc. only insures that they not only take longer to assimilate, in many cases they never do.
The other difference is that a lot of these illegals don't want to become Americans, just live like them. Check out all the Mexican flags/decals on their uninsured heaps.
And unlike the previous waves of Irish and Italians who stayed in inner city ghettos, these Mexican immigrants are spreading their ghettos and ghetto crime to every corner of the country, even rural small towns way out in the country.