Praise be to Allah.
Undoubtedly some children are better than others; this is well known. But the father has no right to show favouritism because of that. On the contrary, he has to treat them all fairly because the Prophet (peace and blessings of Allah be upon him) said: “Fear Allah and treat your children equally.” So it is not permissible for him to prefer one child over another because he is better or honours his parents more. He has to treat them all equally and be sincere towards all of them, so that they will all be steadfast in honouring their parents and in obeying Allah and His Messenger. He should not favour some over others in gift-giving, or bequeath wealth to some of them and not others. All of them should be equal in inheritance and in gift-giving, according to what is prescribed in sharee’ah concerning inheritance and gift-giving. They should all be treated fairly as stated in sharee’ah, so the man has the equivalent of the share of two females. So if he gives one of his sons a thousand, a daughter should be given five hundred. If they are wise and tolerant, and they say, Give our brother such-and-such, and they clearly do not mind, and they say, We don’t mind if you give him a car or whatever… and this is clearly done freely and not because they are too shy or are afraid of him, then that is OK.
The point is that they must be treated fairly. But if they are wise, whether they are male or female, if they have no objection to one of them being given something for special reasons, then that is OK and they have the right to do that.