Neither really. He was a horrible parent to both, and it's awful, but I doubt he really cared for them, but I'll go with Azula here.

I mean at least he didn't burn her face.

^ Exactly.

He never cared for either of them, but it was obvious that Azula was his favorite.

Do any of you guys know what happened to Zuko's mom?

^Spoiler Alert
This may be a bit late, but in The Search, we learn that Ursa was in love before she became Ozai's wife. On the night when Azulon orders Ozai to kill Zuko, Ursa convinces Ozai to let Zuko live by making him a poison for Azulon. Ozai then sends her away because he's afraid she'll kill him with the poison. Ursa goes back to her old lover, who's had his face changed by a spirit, and he brings her to the spirit that can give her a new face to disguise her. Except, the spirit also changes her memory, so she forgets all about Zuko, Azula, and her entire royal life. She settles down and has a daughter. Zuko and Azula eventually find her again and her memory is restored.

As for the poll, I don't think that Ozai cared much for Zuko or Azula.