I've said several times that Azula interests me very much, but so does the whole Fire Nation family. I'm going to analyze stuff, but doesn't mean I'm trying to put things in that aren't there. These are merely observations that I've gotten from the show and theories based off of them.
We know that in the family, Sozin, from Ozai's family, is supposed to be the "evil" side, and Roku, from Ursa's family, is supposed to be the "good" side. So in theory, that would make any offspring of Sozin's inherently evil, and Roku's pure. But what does that make Iroh? He has the same genetic background of Ozai, and yet, he made completely different life choices than he younger brother.
What could have made Iroh like that? I think he's a clear indication that you shouldn't take the genetic "good" and "evil" seriously, but he just used that as example that it might give Zuko a clue as to why he has struggled with his own decisions. I don't think anybody is born evil; it's your upbringing and how your mind reacts to that upbringing. Iroh's mind said 'I don't have to always have to do what my family has done.' The fact that Iroh might have been a prodigy, but wasn't power hungry, he had a different reaction than say, Azula, did.
Azula is also an example that you shouldn't take what Iroh said about Sozin and Roku literally. She has the same genetic background as Zuko, and she has made different decisions, and none of them good.
Ozai might have not been born naturally good at Fire Bending. Or, he could have been a prodigy as well, but since he was second born, Azulon paid Iroh a lot more attention. Let's look at this if Ozai wasn't a naturally good. The fact that Ozai was already born second, and he didn't meet the expectations Azulon already had for Iroh, he was pretty much screwed. So he had to work hard, and try to earn the love his father didn't return to him. Sound familiar?
Azulon probably saw that Ozai had to work so hard to even come close to Iroh, and rejected him for that. As Azula said in CoD "But true power, the divine right to rule, is something you're born with." Points away from Ozai's favor if he was, in fact, not a naturally gifted.
But like I said, we don't know how strong Ozai was in the beginning. From what we've seen in the show. Ozai hasn't seemed to make his own desisions that much. When Azulon told him to kill Zuko, Ozai said he was going to do it. Sure Ozai could have come up with a better option. But in his mind, if he did this, he'd get what he'd want, and didn't even consider the consequences. Ursa was the one to talk him out of it. She came up with another option, and he listened.
If there is one thing Ozai isn't, then that would genre savvy. He was completely surprised that Aang was still alive. He never thought that Azula could lie to him, even though he knows full well how clever she is. Zuko was orginally was like this early on too, but gradually, he has gotten better. We know that Azula is genre savvy incarnate. But what about Ursa? We've haven't seen enough of her to make a completel observation, but Azula must have gotten it from somewhere.
The show has shown us that our decisions play a huge part in our lives. Everyone is capable good and evil, but how we make our decisions is what separates us. Does that mean once someone makes a decision, you can't come back from that? Of course not! Look at Zuko; he spent all of S1 chasing Aang, spent S2 running from Azula, and sometimes going after Aang if they crossed paths, at the end of S2, he has the perfect opportunity to change sides, and, didn't. Then, in S3, he realized that pleasing his father wasn't what he wanted anymore. He figured out his own life purpose, but it took 16/17 years for him to realize what it was.
Does that mean Ozai would want to change sides? Probably not. Why would he? He has all this power and rules the Fire Nation and controls the Earth Kingdom.
Sorry I jumped around a bit; I was having trouble organizing my thoughts. But, as I said in the beginning, these are just theories; I'm not trying to analyze things that might not even be there.