Which is better: giving money to a financially able son to perform Hajj on my behalf after he has already performed Hajj once, or to a financially unable relative to perform Hajj?

If the questioner is unable to perform Hajj due to a chronic illness from which recovery is not expected, it is permissible for him to appoint someone to perform Hajj on his behalf, provided that the proxy has already performed Hajj for himself. This is the criterion for the excuse that validates deputization according to the Shafi'is and Hanbalis.

As for the Hanafis, deputization is permissible for voluntary Hajj with or without an excuse.

However, the Malikis do not permit deputization for Hajj on behalf of a living person at all, whether the delegator is ill or healthy, and whether the Hajj is obligatory or supererogatory.

If the illness preventing a person from Hajj is an ordinary illness from which recovery is expected, then according to the Shafi'is, deputizing someone else for voluntary Hajj is not permissible.

Since deputization for voluntary Hajj is a matter of dispute among jurists, it is better for the questioner to pay the expenses for someone who has not performed Hajj before to perform Hajj for himself, as the permissibility of this is agreed upon by scholars.