There is a Minhag brought in SA OC here to take a chicken on Erev Yom Kippur & perform Kapparos with it. The custom is for a man to take a male chicken while a woman chooses a female chicken to perform the ritual. However, during the times of the Beis Hamikdash, when an individual would bring a Korban Chattas as an atonement for a sin, he/she would always sacrifice a female. See here. Why the difference? Both are being done to atone for a sin?
Because it's not just atonement, but substitution (תמורה). See the teshuvah of the Geonim quoted in Tur Orach Chaim 605, and Bach there.