The Legend of Korra and Avatar the Last Airbender are probably the best Nickelodeon shows of all time. These shows have balanced dark topics with humor amazingly, and have both dealt with trauma and mental conditions.
It wouldn't be right to compare the shows, especially when so different to each other- although still part of the same Avatar world.
The villains were an amazing part of Legend of Korra. In fact, one of the best aspects of the show is that the villains aren't exactly villains. The antagonists aren't just one dimensional characters with almost no depth, like Firelord Ozai, or even Azula- who's character just started to get deeper until we see a complete mental breakdown.
I won't spoil too much, but I'll break down the motives of these Legend of Korra antagonists.
Season 1's Amon wanted equality for nonbenders and benders alike through persecution.
Unalaq wanted reconnection with the spirits through complete destruction.
Zaheer and the Red Lotus wanted freedom through anarchy and chaos.
Kuvira wanted unity and order for all the Earth Kingdom through submission.
The characters making up Team Avatar have a very different dynamic than the original one. Bolin and Mako, siblings Korra meets on one of her first few nights at Republic City. They have depth, though at times, the actual plot could get too riddled up in teen romance and drama.
Korra- Avatar Korra, had started out the show as a headstrong teen, ready to take on the world. She seemed to power her way through everything, and focusing little on the spiritual aspect of her Avatar duties.
Through the course of the show, she had mellowed out in the right way, having an amazing arc as a character. In season 4, her healing arc was one to applaud. After all the poor girl has suffered through, she had to take a break.
The showcase of PTSD was remarkable, and extremely dark for a kids show- yet it was crucial to the plot and Korra's character. The symbolism was everything.
In conclusion- Legend of Korra is an amazing show. At parts, it became a little hard to watch, but the series was definitely worth it. Once you get past Season 1 and 2, I promise 3 and 4 are perfect.