He was never fully able to descend to Azula's level because he always valued at least his own people. This meant that once the propaganda and brainwashing was shown to be wrong, he was more quickly able to switch to the good side.
Asami gave up the only family she had left and her immense wealth and privilege to do the right thing. She chose to risk everything rather than help her own father commit atrocities. And regardless of how much she struggled, she persevered and set out to redeem her family name.