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Hau is a chill bro who sometimes slips in some bants. He meshes well with Gladion, and he has strong interactions throughout the game. He fits the feel of the region and he's really likable overall despite being another nice rival. It all flows well with the game's narrative. Though I wish they had done more with him being jealous about Tapu Koko choosing you over him. Barry is an impatient, and overly determined but slows down once those traits lead to him failing to save Uxie.
They're not alike but both are examples of what a "nice" rival should be. For Hau it's how his personality fits into the region's overall culture and contrasts with the other rival (Who he gets to spend a decent amount of time with and also bring character out of), and for Barry it's how his growth isn't related to just losing to the player so you never feel like a bully.