Is it permissible for him to take Hajj expenses from his father?

There is no
reason why a well-wisher should not donate Hajj expenses to someone, and it
is not a condition of obligatory or naafil Hajj being valid that it should
be paid for with the pilgrim’s own money. 

If this
donation is given to a relative, then the reward is greater, and he will
have a reward like that of Hajj, in sha Allaah. What your father is going to
do, paying the expenses for Hajj for you and your wife, is something that is
to be appreciated, and he is included in the words of the verse
(interpretation of the meaning): 

“Help you
one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety)”

[al-Maa’idah 5:2]

There is no
difference between the two ways mentioned in the question. If you have not
done Hajj before then this Hajj will be the obligatory one, and it will not
be naafil just because your father donated the expenses. 

In the
answer to question no. 36990,
we have quoted a fatwa from the scholars of the Standing Committee
concerning this. Please refer to it. 

Your father
who is going to donate this money should have performed Hajj already,
because the command is addressed to him too. 

It is not
right to delay Hajj then appointed help someone else to do Hajj, rather he
should hasten to do Hajj himself, then if he has any extra money he may help
you to do Hajj. 

In the
answer to question no. 36637
we have quoted a fatwa from the scholars of the Standing Committee
concerning this. Please refer to it. 

One
indication that it is permissible to do Hajj with money other than one’s own
is the fact that it is permissible to give zakaah to a poor person so that
he can do Hajj. This is included in the verse in which Allaah says, listing
those who are entitled to zakaah, (interpretation of the meaning): 

“and for
Allaah’s Cause”

[al-Tawbah 9:60]

that
includes both jihad and Hajj. 

This has
already been explained in the answer to question no.
40023. 

And Allaah
knows best.