Because Zuko had love and she didn't. She had her father's favor but he didn't love her. Iroh and Ursa showed Zuko love and never did with Azula. She lost her childhood friends and Zuko gained friends in the world, she had a dream her entire life that Zuko took away from her, and unlike Zuko so far her story doesn't have a happy ending.

At least Zuko was happy in the end.

They are both tragic!
Azula didn't realise, that her mother loved her much as Zuko. Beacuse of that, she get a little bit (cough*) psycho.
Zuko: You know the story!

zuko finds happiness but azula has a ddetrimental ending for her last scene...

Zuko for most of the series, but Azula at the end. She never had love in her life or fulfillment besides wanting to rule the world, but she didn't realize how little that actually meant until the very end of the series. That was so much a shock that it literally made her insane.

Zuko's life

zuko, regardless of how tragic or who had it worse you all choose your own paths, zuko was walking the same path as azula but in the end he chose to walk his own path and find his own destiny, azula chose to keep her tragic path into insanity, she's had numerous times to redeem herself and just didnt take it and keep things how they are which resulted in her mental break down, zuko may have been shown love but he was always put down by azula and their father, the two ppl he wanted acceptance from only used and banished and manipulated him for most of his life, and his father was going to kill him, some may disagree but yeah zuko had it way worse only thing is that zuko got a happy end instead, but everything that ends happy doesnt start off happy

She didn't exactly have someone to guide her on the right path like Zuko did with Iroh. It's hard for someone to change after years of being taught a certain way.