I believe that the two series, although extremely different in plot aspects, work amazingly well with one another, producing a quite common relationship between sequeling pieces of literature, or in this case, television series. While looking at the Last Airbender series from a Legend of Korra perspective, one can view the former as a history book, filled with many intriguing stories, life lessons, and interesting facts, as well as an incredibly amazing underlying plot line that is able to captivate the viewer's attention for three entire seasons. However, one sees this as a past world with few remnants still existing in the current world, and one begins to wonder how to deal with the problems of the present given this knowledge of the past. This occurs inas Korra must fight against something that she first identifies as a completely unrelated problem to that with which Aang had to deal, since Korra is fighting "non-benders," to keep balance in the world but the problem is revealed to be quite similar. This is not only because Amon turns out to be a bender whom Korra must fight (similar to Aang fighting Fire Lord Ozai), but more importantly because of the underlying fact that the same situation is present here, where an entity (Amon/Fire Nation) is invoking harm on others in a greedy pursuit to gain power. Knowing this makes these plot differences in less obvious and overall easier to understand. However, I realize the fact that there do exist major differences in society from what we have seen of Korra’s time compared to the time when Aang was the Avatar. This can be explained by the aforementioned comparison of ATLA to a history book, or for a more concrete reference the two series have a relationship to each other similar to that between the Old and New Testaments. The Old Testament consists of stories and accounts of major events that are significant to the Christian and Judaic realm, just as ATLA gives us the entire structure of the Avatar world upon which many concepts are built that make up the essence of all things Avatar including this Wiki. On the other hand LoK produces a sort of reality check by uncovering age-old problems that are hiding under new disguises in the modern age, as well as some new issues that arise in society. Similarly, the New Testament provides Christians with specific problems prevalent in the church at the time when it was written, as well as nowadays, and shows how they relate to problems of the past and how to solve them. A specific example of a major societal shift that greatly impacts the world of Avatar is the concept of industry and the Industrial Revolution. Industry has a recurring bad connotation, starting with the Fire Nation’s embrace of industry, followed by Sato, head of Future Industries, turning out to be an Equalist, and of course the Equalists consistently getting better technology that is used to get an upper hand on the protagonists. Despite the attempts of Team Avatar to use technology to help them beat the anti-bending revolution, we always see that technology used in more bad ways than good (take that as you will). We also see many other changes in the society of the Avatar world that all have both advantages and disadvantages. For example, there is a gender shift, the development of more a advanced and complicated civilization, and a progression in the normality of previously exclusive bending techniques (e.g. lightning). Many of these changes from Aang to Korra are made more noticeable because of the seventy-year time lapse and we see the great leap that society takes rather than the small shifts that we see in our own society.
I am a bit long-winded, but please comment with your thoughts, and don't be afraid to respectfully disagree, I like seeing other viewpoints. Thanks for reading!