Praise be to Allah the Lord of the Worlds.
A son is an extension for his father because he is part of him. Specifying the son in the afore-narration is based on the fact he is the closest to his father and the most entitled to pray for him, because the deceased benefits from the prayer (supplication) of anyone.
The piousness of the son is a gift from Allah the Almighty and good parenting is a key factor in that. The prayer mentioned in this narration is meant to motivate children to do as many righteous deeds as possibleon behalf of their deceased parents.
Preferring an act of worship over another is a difficult task because all these acts are greatly rewarded by Allah. The most important of these is continuous charity, prayer, reciting Quran and giving rights to whom they belong. Abu Hurairah (May Allah be pleased with him) reported: "The Messenger of Allah (PBUH) said: "When a man dies, his deeds come to an end, except for three: A continuous charity, knowledge by which people derive benefit, pious son who prays for him." {Muslim}. And Allah the Almighty Knows Best.