While the immigration policy in the U.S. is mainly oriented to family reunification, in Australia, Canada and the U.K. it is a points-based immigration system which main objective is to attract high skilled immigrants. This paper compares both immigration policies through the transition for the U.S. and Mexico. I find that: (i) The point system increases the average years of the immigrants by 3.5 years. (ii) The Mexican immigrants suffer a 10% reduction in their effective hours of labor when they move to the U.S. (iii) Migration reduces inequality, more significantly if the immigration policy is the point system and increases output per capita differences between both countries. (iv) The offspring of the immigrants invest more in human capital than the U.S. natives. (v) The earnings ratio immigrants to the U.S. natives is lower under the quota system than under the point system but along the transition it reverses converging at the steady state.