Avatar: The Last Airbender knew how to make an event out of Aang entering the Avatar State. Anytime Aang's tattoos began to glow and the four elements came together, viewers knew they were in for a treat. But as enjoyable as those scenes may have been, they often put the protagonist in a needless amount of danger. Avatar Korra's usage of the Avatar State may have been less showy, but it was a whole lot wiser.
Early on, Aang's mistakes are understandable given how very little control he has over the Avatar State. Generally, it activates as a form of self-defense or during states of extreme emotional duress. And, as spiritually-attuned as Aang was, he was still just a kid and, thus, had big emotions -- meaning he wasn't entirely equipped to fight off the Avatar State most times it came over him. The help of someone he cared about, like Katara, talking him down often helped ease the Avatar's out of it, but beyond that, there wasn't much control.
By the second season Aang comes to appreciate the true importance of the Avatar State. It grants its user greater power as well as the wealth of knowledge from all past Avatars, putting them into a trance-like state where they become a force of nature above all other benders. It comes with a devastating limit, however, as the previous Avatar, Roku, warns Aang that dying in the Avatar State would end the Avatar Cycle altogether. It would be a blow to the balance of the world not only for Aang's lifetime, but for all future generations.
Even with that knowledge, however, and even as Aang begins to gain mastery of the Avatar State, he continues to wield it fearfully, almost never willingly embracing the power. At first, he closes himself off to it altogether, shirking Guru Pathik's advice that he needed to let go of his connections to those he loved, but shortly after that Aang realizes during a losing battle in the crystal catacombs beneath Ba Sing Se that he needs the Avatar State in order to win. He enters into it, ascends above all combatants present... and dies.
It's only through Katara's intervention with water from the spirit oasis that the Avatar line did not end right then and there. The moment underscores the extreme risk that balances out the extreme reward of entering such a powerful state, but it also justifies Aang's fear of it and why he refuses to master it the way he should. Although the Avatar State is completely closed to him immediately afterward, as soon as he unlocks it in his fight with Ozai, he begins to use it in the same way. There's not even a question of control -- Aang ends and reenters the Avatar State at will once it's unlocked in his final battle, and in most subsequent uses in the comic stories that followed he continued to use it in the same way.
Korra, on the other hand, shows off the alternative perfectly. Although Korra has her own difficulties mastering the Avatar State early in her career as Avatar, she does not show Aang's same proclivity for emotionally charged entrances. Throughout most of the first season, she doesn't enter it at all, and in the season that followed, once she did unlock the Avatar State she generally used it in far shorter bursts.
Korra's style tended more toward brief charge ups of power fueled by the Avatar State. On one hand, you could call her use of it overkill, as she would break it out during moments with lower stakes -- like an air scooter race. However, on the other hand, you could also say that Korra actively chose to use the Avatar State in a much safer way. In her fights against spirits, or escaping the Northern Water Tribe's barricade, or especially in her series finale fight against Kuvira's mech, Korra showed just how useful brief surges of power could be. She could bend vast volumes of each element no other bender could match, and call on the Avatar State again whenever needed.
In the Avatar State, Korra could sweep battleships out of her way or send an entire river 25 stories into the air before freezing it into a massive wall of ice. One of her final acts of the series involved a brief pulse of the Avatar State to repel a beam of energy from Kuvira's energy canon, showing that she could make the Avatar State work for her, whenever she wanted. Aang's fear of the State meant that he only entered it when he had no other choice — and, often, the Avatar State would force itself on him. Korra, however, showed no such fear and, as such, was able to call on it at will much earlier into her Avatarhood, making usage of it far more akin to most past Avatars. Roku, Kyoshi, Kuruk and Yangchen were all shown in their adulthood to use brief pulses rather than sustained states. Though, to be fair, so did Aang in his own adulthood.
The only time Korra entered a sustained Avatar State rampage akin to Aang was when the Red Lotus poisoned her, forcing her body into it as a defense mechanism. Even still, Korra still managed to fight it off and hold it back. In almost every instance, her use of the Avatar State compared to Aang is far more considered and tactically sound. All she had to do was embrace her power, rather than fear it.