My new home already has a hood vent for the range.

The poupose of either is to eliminate any smoke created by the range or grille and move as much of the cooking odors to the outside. I wouldn't use both at the same time, but if the hood is vented to the outside, it would be just fine to use only the hood. Aregular cleaning will be necesssary. The downdraft has limits as to the distance it will efficiently exhaust air. Flex hose should not be used. And excessive bends or vent length, cuts into the efficiency.