Avatar: The Last Airbender

Bluey is a show that tries to, and also successfully does, appeal to children and to parents. It doesn't try to be anything more. It's lighthearted and fun and that's all it's supposed to be.

Avatar on the other hand is a kids show that also wants to appeal to pre-teens and teenagers. Some of the themes of Avatar are not really kid friendly: the genocide of air benders, Zukos father mutilating him to make an example, Sokka losing someone he loved. Those are examples from the first season that I remembered. Avatar has a lot of mature subjects. There's a reason the legend of Korra targeted late teens and young adults, because the more mature subjects of Avatar were what made the show great and the audience grew up.

Overall Avatar is the better show, but Bluey is the better kids show.

The only episodes of Bluey that I’ve seen are the cricket one and the State of Origin one, so I don’t think I’m best-placed to answer, but I would say it’s slightly more than @GoodEye8@lemm.ee gives it credit for. It helps role model good parent-child relationships, engages with adults emotionally. But unlike Avatar, which engages you emotionally entirely on its own merits, Bluey engages with your inner child or your parental instinct in an amazingly effective (but quite different and difficult to compare to Avatar) way.