This is a battle of gravity fighters. Kat uses gravity to amp up her physical abilities and move at super speeds while Haiji usually uses it more for projectiles. Although Haiji can use it physically as well and was even able to lift an entire chunk of a building. He just seems to be able to use it at a much higher level than what we’ve seen Kat do. While she may be able to put up a decent fight at first, the match is over once Haiji uses his Hungry Joker form. Haiji (Hungry Joker) wins.
Suggested by iKnowledge Dr. Polaris and Kat both have impressive abilities but Kat has mastered her techniques to a whole other level. Polaris has magnetism which he can use to repel fighters or bring them in close but he doesn’t have a lot of close combat options. Meanwhile Kat can control her personal gravity and emit it while landing quick hits at a rapid pace. Polaris would very quickly be overwhelmed in battle and would not last long here. Kat (Gravity Rush) wins.