All of the differences are based upon the fact that one person obeys the labor and tax laws, and the other does not. Immigration status really doesn’t give Jose any sort of advantage. Joe could choose to be “illegal” also, even though he is a citizen. For example, Joe could choose to get paid under the table, or choose not pay for car insurance either. (And lots of Joes do just this.)

Except that being a Mexican citizen, Jose could just head home. No extradition treaty with Mexico. Later Jose could head back over the border as ‘Manuel’, and no ones the wiser.

There is definitely a problem with a lot of Joe(s) taking money under the table. The fact that a lot do, does not make it right nor does it make the problem that Jose causes any less.