To Answer your "why execute" question :
A person who leaves his Islam after accepting it is executed in a country ruled by Sharia or Islamic state (I stress, Islamic state) by the decision of the ruler of the land in consultation with the scholars who examine the evidences and conditions of apostasy. Obviously, this ruling can only be implemented by the judge in a state that rules by the sharee`ah law.
This is the ruling of Allah and His Messenger, as the Prophet (peace and blessings of Allah be upon him) said:
"Whoever changes his religion, kill him." (reported by al-Bukhari,
al-Fath, no. 3017)
The one who has known the religion which Allah, his Creator revealed, entered it and practised it, then rejected it, despised it and left it, is a person who does not deserve to live on the earth of Allah and eat from the provision of Allah.
By leaving Islam, the apostate opens the way for everyone who wants to leave the faith, thus spreading apostasy and encouraging it.
The apostate is not to be killed without warning. He is given a last chance and he is given three days to repent. If he repents, he will be left alone; if he does not repent, then he will be killed.
Now, let me ask you a question: As I said before this is done in a land which is ruled by the law of Allah. Basically, the whole legislation is what Allah revealed. Now, if a person leaves Islam after believing it, it is not only apostasy but also rejecting/betraying the law/constitution - or whatever you want to call it and an act of treason. Even after that he is given three days to repent and change his decision before he is executed.
Now, which country in the world allows you to reject the law of the land or betray or commit treason and still move around the country freely? Makes sense?
As for the difference you mention:
There is an Ijmaa (consensus) of the scholars that the apostate is to be killed and there is no doubt about this. He is given some time to repent and if he does not turn back to Allah, he is to be executed by the judge. And note again: this ruling can only be implemented by the judge in a state that rules by the sharee`ah law.
The only different view was that of Hanafi madhab which says women cannot be executed. But, most of current Hanafi scholars agree that even apostate women should be executed. So, it is very odd rare view. Other than that, everyone agree, the person, where man or woman should be executed.
Credits: Used some points from Why death is the punishment for Apostasy