So far, I really enjoy the Legend of Korra. It takes the world that Avatar built and expands upon it. And it's showing the difference between technology and spirituality in the world. It's obvious that all future Avatars will have to try to maintain a balance between the two in the world. Allow technology to flourish for the sake of all, but also make sure that people respect nature and the spirits.
I personally hope that all the following Seasons of Korra will be self contained stories. I think it would be interesting to see more than one battle. It's obvious that Aang fought many battles after the Fire Lord was defeated. And, I hope that we see multiple different battles. I think that would be interesting.
As for Korra's personality, I think of it as such: Korra knew she was the Avatar from an early age.
There's a reason they waited till the Avatar became of age to tell them. It's a lot of responsibility to be the Avatar. People all over the world look to you for guidance, help, and leadership. Not just for one nation, or one people, but for the entire world, human and spirit.
In addition, her entire experience has been people telling her, "You're the Avatar, so you're great and powerful. The most powerful of all. Don't let that go to you head."
How would do you think a person would grow? I'd say they would be headstrong and arrogant. But Korra also shows a true willingness and desire to help others. I think that is something to her credit. She wants to do the right thing, but it's not that easy. She's had several people disrespect her and even some she trusted had lied to her. And she feels that no one is letting her do her duty, the one they were telling her about her entire life. How would you feel if the same people who were preparing you for greatness were now telling you that you were ready? Aang wasn't ready.
I can see why some people don't like her, but I have no problem with her. It would have been far too easy to make her Aang 2.0, but they didn't.
So, yes, comparing Aang to Korra is wrong. Aang was a monk trained to be an Air Nomad. He never wanted to be the Avatar. Never even suspected that he was. And when he learned that he was, it threatened to take everything away from him. His friends, his master, his entire way of life. Aang had strong spiritual training from an early age. He was taught to be detached and separate. Korra was kept separate, detached from the world, and embraced her role as Avatar. It gave her life meaning. There are huge difference in the characters and their pasts.
Oh, and as for the Avatar State, I think people are right and wrong. Early on Aang could not control it. It was stated to be a Defense System for the Avatar. It activated whenever the Avatar was in mortal danger and empowered them with the skill, power, and knowledge to escape that danger. Aang was shown to have little to no memory of what he did at those times. And certainly no control over it. And that scared him.
Later on, he mastered the Avatar State and could control it at will. He could enter it for extended times to utilize great power, or store a "charge" for immediate use for a single act, like causing the river waters to rise and put out flames from his battle against the Fire Lord.
Korra can currently use the Avatar State at will. But that doesn't mean she's perfect in the state. That would be boring, would it not. She's still in control and acts as she would. The reason she doesn't seem to explode with power is simple. Avatar State doesn't do that. Why wouldn't Roku have simply used Avatar State to calm the volcano? Because even the Avatar can't do that.
The Avatar isn't unstoppable. A truly skilled and powerful bender can be their equal or close to it. Remember Toph and Katara?
Beyond that, I had a feeling they were going to reveal what they did in the last episode. I started thinking that near the start. That things seemed a bit curious with how things were going. As for his motivations, I can't guess at. But I suspect that he's not quite the patriot that we were led to believe.