Apparently Zuko is not just weak just in terms of his fire-bending.... but he's also weaker than her in terms of emotional strength. Then again girls in their growing age tend to be faster learners and mature faster than the boys around their age.... and in the case of Zuko (who is only around 1 or 2 years older).... the fact that his father kept showing favouritism to his sister.... matched by his disgust over Zuko.... would've made it impossible for him to grow up without personality issues. The moment he was able to control his anger only then was he able to defeat Azula.

So yeah in simple terms.... Zuko would not have the cool-headedness to stop, calm-down, think, relax and then give a scathing retort to Azula.... not that it really mattered. She's vicious and has thick skin. Maybe because Zuko has empathy and Azula does NOT.... that could explain why he orients towards thinking from what others think.... Azula on the other hand does NOT care.... at least knows how to put on a good image.

Have you seen how Iroh behaves.... he's probably the most cool-headed person there is and thereby the most emotionally tough... thus that explains why he is probably one of the strongest Fire-benders alive during his time. That again... because he's an experienced middle aged man. But the point is because of his cool-headedness he was able to not only re-direct lightning from other firebenders.... but he is also able to generate his own lightning.