From an interesting op-ed in today's Washington Post by Christina Boyd and Lee Epstein.
a diverse Supreme Court isn't just about a bench that looks like America. This is about jurisprudence, too. In research that we conducted with our colleague Andrew D. Martin, we studied the votes of federal court of appeals judges in many areas of the law, from environmental cases to capital punishment and sex discrimination. For the most part, we found no difference in the voting patterns of male and female judges, except when it comes to sex discrimination cases. There, we found that female judges are approximately 10 percent more likely to rule in favor of the party bringing the discrimination claim. We also found that the presence of a female judge causes male judges to vote differently. When male and female judges serve together to decide a sex discrimination case, the male judges are nearly 15 percent more likely to rule in favor of the party alleging discrimination than when they sit with male judges only.
This holds true even after we account for judges' ideological leanings. If Obama is considering two fairly moderate people, one a woman and the other a man, we would expect the woman to cast more liberal votes in sex discrimination cases. The same would be true if the president were considering two very liberal candidates, again, one a man and one a woman.
UPDATE: In a related vein, here's a student note finding a statistically significant difference in the way male and female judges handle cases involving sexual orientation.