If a person divides his wealth among his children during his lifetime, should he divide it equally among his sons and daughters?

It is the duty of a father to bring up his children while maintaining equality between them. This applies to everything that helps them through life, whether moral or material. It is not permissible for a father to show favoritism to one of his children. In some communities, sons are given preference over daughters. In Islam, this is not permissible. If a father gives his son a good education he must his daughter the same. Similarly, if a father gives a gift to one of his children, he should give similar gifts to the rest of his children, sons and daughters alike. Some people think that since the shares of inheritance differ between sons and daughters, gifts can also differ and they give their daughters only half of the gifts they give to their sons. This is a wrong approach because the needs of children in life are equal. And because they stand in the same relationship to their father, total equality should be maintained between them. Gifts cannot be treated as inheritance because the death of a father places certain responsibilities on his sons but not on his daughters.

The principle of equality relies on the following hadith which we often quote. An-Nu'man Ibn Bashir reported that his father took him to the Prophet (peace and blessings be upon him) and said: 'Messenger of God! I gave this son of mine a slave as a gift and I wish that you to bear witness to it.' The Prophet (peace and blessings be upon him) asked him, ‘Did you give each of your children a similar gift?' 'No,' he said. The Prophet (peace and blessings be upon him) said, 'Then seek for yourself some other witness because I do not witness injustice' " [recorded by Al-Bukhari and Muslim]. It is to be noted that the Prophet's question to his Companion inquires whether he had given each of his children, not each of his sons, a similar gift. When we deduce a ruling on the basis of a Quranic verse or hadith, we must bear in mind that every word it includes is deliberately chosen to convey an intended meaning. The Quran, God’s word, does not admit any deficiency or error. It is not possible to assume that anything has been missed out, overlooked or forgotten. God the Almighty does not forget anything. Similarly, when the Prophet (peace and blessings be upon him) gave rulings on particular incidents, he did so on the basis of revelation, which he received from On High. Therefore, his statements must be treated as having been carefully considered. The fact that the Prophet (peace and blessings be upon him) asked his Companion whether he had given each of his children similar gifts, means that the question applies to sons and daughters, since the term "children" includes both. Had it been the case that gifts should be treated in the same way as inheritance, the Prophet (peace and blessings be upon him) would have outlined it.
In the light of the above, the answer to your question is that if a person wants to divide his wealth among his children during his lifetime, he should do so on an equal basis.