Lin Beifong, after seeing Korra fight in one of her Pro-bending matches, tells Tenzin that she "can't believe your sweet-tempered father was reincarnated into that girl." Truer words were never spoken — Avatar Korra is unlike her precursor in many ways, from her personality to her philosophy.
It's a great decision made by the showrunners, to be honest, as it renews the perspective used by The Legend of Korra. More importantly, it shows that the Avatar can be reincarnated into a wide variety of personality types and that the process is independent of any explanation that humans can come up with.
She Is A Lot Tougher
If there's one thing that can be learned from Korra's various fights, it's that she can take a beating as hard as she can offer one. Aang's Air Nomadic lore prevents him from using offensive abilities in favor of defense or escape, but she is not restricted in any such way.
Further, Korra is strong in the literal sense, given that she can carry extremely heavy objects with ease, scale complex cliff-patterns without premeditation, or even destroy bending attacks with her bare hands. In contrast, Aang rarely bothers fighting with his body, instead replacing his techniques with a bending style.
She Is Considerably Older
OK, so she's barely got five years on Aang, but the gulf between 12 and 17 is as vast as that between 25 and 50 in of experience. For example, the young Airbender spends half the narrative mooning over Katara, while Korra just goes for the "kill" the second she finds someone she's attracted to (Mako being the first of her conquests.)
Her age, combined with the fact that she is able to bend three elements by the time she's five years old, gives her the added advantage of time that Aang did not receive when he was hatched from his iceberg.
She Will Do What It Takes
Korra's temper notwithstanding, her perseverance and mental fortitude greatly outshine that of the previous Avatar: she often rejects the advice given by her seniors in favor of her own intuition.
This generally holds her in good stead, like when she opts to save Kuvira rather than condemning her to the horrors of the Spirit World. However, Korra has taken her self-reliance too far on several occasions, like when she rudely denies her parents' opinions against her uncle, Unalaq, and goes on to help him open the South Pole portal
She Is Not As Mischievous
Korra is more, for want of a better word, mature than Aang, given her predilections towards dating and relationships right off the bat. She also takes being an Avatar seriously, training for several years before she even goes to Republic City to begin her first arc (while Aang prefers to go into hiding instead of taking on the Fire Nation as was his duty.)
Korra might be whimsical and playful, but she keeps these traits of hers in control — it is very unlikely that she would go hunting for random animals to play with when there are more pressing matters at hand.
She Meets Raava
The second Avatar to come in with the Spirit of Light is Korra, an event that occurs during Harmonic Convergence when Unalaq helps free Vaatu from his Tree of Time prison.
This is a momentous milestone because there has been no other Avatar known to have had any affiliation with Raava since Wan, over ten thousand years ago. Korra not only converses with her directly but also saves her from being utterly extinguished by her dark half (with a little from little Jinora.)
She Can Metalbend
Along with the previous entry, Korra's Metalbending makes her one of the most, if not the most, unique Avatars in existence; which is saying a lot because there have been around 130-180 of them since the position was first established.
She learns the art from Suyin Beifong, Toph's younger daughter, first practicing on a meteorite before moving on to more complex procedures. Aang could have picked up the style, technically, although it is clear that he never did ("What I'd give to be a Metalbender.")
She Loses Her Past Lives
When UnaVaatu takes its rage out on the already weakened Raava, each attack that shatters the Spirit of Light simultaneously breaks the connection between Korra and every single Avatar living within her, starting with Aang.
Unfortunately for her, she is unable to regain this bond even after reviving Raava within herself, meaning that she will never again be able to receive advice or manifest her past lives. Interestingly, this doesn't mean that the Avatar cycle has been destroyed, only that it has been started from scratch.
She Is A Superior Fighter
Korra is able to dispatch villains with mere flicks of her wrist, and that too without using a shred of bending. Her superior reflexes and speed enhance her offensive attacks, while her stability and nimbleness come in handy whenever she needs to employ defensive modes in combat.
Korra uses the environment to her benefit as well, for instance, when she employs Mako's red scarf or her own armband to instantly turn the tides of battle in her favor. If this isn't impressive enough, Korra has shown herself capable of overcoming multiple opponents trained in chi-blocking, a technique that Aang often found difficult to counter.
She Can Heal Others
Korra's Waterbending is at the core of her powers, being from the Southern Water Tribe, which means she can easily employ it as a form of healing (taught to her by Katara, who was the only paramedic available to Aang during the Hundred Year War.)
She has been able to use the skill as an analgesic for Bolin's shoulder, as well as almost completely heal General Iroh's extreme burn injuries. With Unalaq, Korra also picks up Spiritbending, an extension of the same style, which she finds difficult at first but soon masters.
She Is A Realized Avatar
Aang uses the entirety of his arc, all the three Books, to reach a able Avatar State, but Korra attains this evolution by the end of Book One: Air. In fact, she can flip between the two phases voluntarily, which is the defining marker of a fully realized Avatar.
Nevertheless, Korra doesn't always live up to the mark in this regard, but this has more to do with Zaheer and co.'s mercury intoxication than her own inability. In any case, her transition into the Avatar State is not based on the flux of her emotions, like Aang's tends to be.
