I went to Northwestern as an undergrad and Berkeley as a grad student. Both are excellent schools, however there are significant differences.
Northwestern's student body is relatively homogeneous, white, affluent, preprofessional. Berkeley is more diverse and probably better known internationally.
At the undergraduate level overall, there is a higher mean and lower variance in terms of the quality of the NU students. The average student at NU is probably better than the average student at Berkeley, but the best students at Berkeley are better than the best students from NU.
NU's business and law schools are better as are its journalism and theater programs. Berkeley is among the best in the world in science, engineering, and many humanities and social science fields, especially at the graduate level.