I feel like Kadaj would really like Sonic but he'd have to do the whole 'faker' thing with Sonic and challenge him to pointless races around areas, Kadaj would obviously be slower.
So they'd have a rivalry going until they needed to work together on something or against a greater enemy and then Kadaj would learn how to become best friends instead. And Kadaj would realize he doesn't need to be a super speed hedgehog to be Sonic's friend.