Despite sharing the same world, in a lot of ways Avatar: The Last Airbender and The Legend of Korra were completely different stories reflected by contrastive Avatars. Whereas Aang was an outright pacifist, reluctant to embrace his role of Avatar and prone to enjoying the lighter sides of life, Korra was an often aggressive and confrontational Avatar who eagerly dove into her destiny from an early age.
Considering he was ultimately successful, in many ways it's hard to fault Aang's approach to his primary mission to end the Hundred Year War. Yet in comparing the two, it's hard to escape the feeling that Korra may have done an even better job. What if it were Avatar Korra, rather than Aang, whose mission was to defeat the Fire Lord and restore balance to the world?
Aang was a wonderful protagonist to introduce audiences to the world of Avatar, making for a unique and refreshing character who defined much of what made the original series great. That said, there was much to be desired in the fulfillment of his duties that begs the question of how the world may have been better off with a different Avatar in his role. First learning he was the Avatar at age 12, Aang initially ran away from his home and became frozen for 100 years -- during which his people were wiped out. Even after his awakening, he took months to embrace the importance of the responsibilities ahead of him.
In stark contrast, at the age of four Korra declared "I'm the Avatar! You gotta deal with it!" and was already bending three different elements at once -- eight years ahead of when Aang first expanded beyond his own native element of air. The problems in Korra's time were the opposite of Aang's, with much of her arc revolving around her need to accept her vulnerabilities rather than her responsibilities. But in her eagerness to fulfill her duty, she could very well have succeeded in many of the places Aang failed. She would have embraced her training at an age before Aang even knew he was the Avatar, and would have mastered the elements far sooner.
Aang was hesitant to ever firebend again after his first day producing flames saw him injure his friend Katara. He had yet to master it even by The Last Airbender's finale, with Toph noting that Aang's earthbending could still use work by that point. While Korra starts at an older age than Aang -- having already mastered three elements -- it's not a huge leap to assume the Hundred Year War would have accelerated her training compared to her peaceful, isolated upbringing in the White Lotus compound. If her skills alone were not enough to defeat Ozai during a climactic final battle, her comfortable mastery of the Avatar State soon after gaining it would surely have won her the day. Aang shirked the Avatar State as a resource, seldom controlled it, and his world was lucky that fortune allowed him to use it at all.
Korra's mastery of the Avatar State was a valuable asset that she could've used in defeating the Fire Lord, but given her proactive approach to saving the world, it's likely she wouldn't even have needed it. The urgency in The Last Airbender's finale resulted from the arrival of Sozin's Comet -- which empowered the Fire Lord thousands of times greater than he was before -- but Korra would never have been so non-confrontational as to wait until the last minute for a final duel. Heck, she directly challenged Amon to a duel as early as the second episode in Legend of Korra.
This is not to look at Korra's approach to being the Avatar with rose-tinted glasses, or to pretend she had every advantage over Aang. Indeed, much of Aang's value to his time came in finding nonviolent solutions to problems Korra would likely have exacerbated with confrontation. Many of the smaller adventures Aang resolved on his journey, such as the feud between the Gan Jin and the Zhang tribes, would likely have been worse off with Korra's head-on approach.
Then there's the ultimate question of whether or not Aang's nonviolent solution to his battle with Ozai -- in which he removed the Fire Lord's bending -- was the best one. The core issue of The Last Airbender's finale questioned whether it was permissible to take a life, but Korra seemingly shared no such qualms as she and her allies threaten and kill various villains during Legend of Korra. With the Hundred Year War ending in Ozai's death, the world of Avatar would have been far different. Yet in some ways, it's hard to say that ending the war earlier would definitively be a worse option.