From The Undercover Economist by Tim Harford:
New workers are good for people who have assets that become relatively scarcer. In fact the people who are most harmed by new immigration are the previous group of immigrants who find their wages nailed to the floor.
Skilled immigrants lower the wages of skilled natives and unskilled immigrants lower the wages of unskilled natives.
Allowing lots of skilled immigrants will help control the gap between skilled and unskilled wages while allowing unskilled immigrants will do the reverse.