Earlier, I talked about the priesthood. The Catholic Church teaches that a man's soul is changed, when he becomes a priest. Specifically, an unremoveable mark is placed upon his soul. This is what allows a priest to distribute the sacraments, which is the primary function of a priest.
A key point that I emphasize is the fact that a priest produces the sacraments in the person of Christ. This is not symbolic or figurative. The priest literally becomes Jesus Christ, at the moment a sacrament is produced. When he says, "I baptize you" or "this is my body" or "I forgive you", that is not the priest speaking. It is Jesus speaking (hence the switch to first person). Only Jesus' power can produce a sacrament. A priest cannot produce sacraments, out of his own power.
What is a consequence of the fact that priests work in the person of Christ? One is that priests have to be male, because Christ was male. Both male and female can represent Jesus; only male can literally be Jesus. That is the official teaching of the Catholic Church, in regards to producing sacraments.
Earlier, I stated that men's souls are different from women's souls. The Church has not said anything on the subject, but we can use logic here. Becoming a priest leaves a mark on the soul. Only men can become priests. Therefore, only men's souls can receive the unremoveable mark of priesthood. That is one difference between men's souls and women's souls.
To be honest, that's probably the only difference between men's souls and women's souls. But this is just me talking here, not the Church. We know there are differences between men's bodies and women's bodies, and we know that the body can affect the soul (and vice-versa). Therefore, it is possible that a female body causes the soul to develop differently than a male body does.