Anon asked: Do you think Azula and Zuko's relationship would have been different if she was the older sibling?
A little. Since she'd be older and the Fire Nation doesn't seem to have a problem with women being heirs (if they did, Ozai would have had to get remarried once he banished Zuko. And when he tried to get his father to revoke Iroh's right to the throne he said "My children are alive" and not "My son is alive") she might not see Zuko as that much of a rival. She'd be eldest child AND the prodigy, so no rivalry over political power, just over their parent's affection. And while Zuko still resent her, it'd probably be a little "expected" that she was better than him, so Ozai could end up being just a little less demanding of him (but just a little, because he's still Ozai).
Azula would probably be a little less mean to him since she doesn't really need to fight him - she already won. And I wouldn't be surprised if Zuko really looked up to her before their father realized he wasn't a prodigy like Azula and started punishing him for it.
Overall, their dynamic would be less antagonistic, and their rivalry would take longer to really start.