I think that Sparda being controlled by a more powerful demon, forced to fight his son, sounds like a very cool idea. It is a bit cliché, but also very powerful, as we will see how their relationship, like we did with Dante and Vergil in Devil May Cry 1 where Vergil was controlled and used as a weapon against Dante.
Sparda made Hell his bitch, ruled the human world for some time, faded away as myth, had the Order of the Sword worship him as a god and you expect that a random demon coming out of your fantasy imagination can be capable of controlling the Legendary Dark Knight.
why would Vergil be closer to Sparda? Vergil is trying to gain absolute power and open the gate to the demon realm which is the polar opposite of Sparda.
That doesn't make Dante more suitable to be closer to Sparda.
Sparda is a demon. Vergil prefers his demon heritage over is human side.
Personality wise, I'm sure that he is cold and level headed like his first born, Vergil.
Sparda pitied humans because they couldn't defend themselves against the demons invasion. Vergil considers humans as weaklings.
The only thing that Sparda and Dante share in common, is the will to fight for humans who are oppressed.