I think it's only natural that the Slytherins would work through connection networks like the Wizarding World in general does according to [Unknown site tag]'s theory. After all, most of the Slytherins, if not all, are either pureblood or halfblood, and they already have a connection to the way the WW works through their families. The Gryffindor seems to attract more Muggle-born students, who don't have the cultural background and the family connections to belong to existing networks.

I think the Slytherins would accept authorities and leaders more easily than the Gryffindors because of the hierarchy they are used to and they are not loyal to individual as much as they are loyal to their networks (families being the closest network they belong to), whereas Gryffindors would follow someone who is a charismatic leader. I think Harry has the potential to become such a leader if he just took the position.