These two animated series are Samurai Jack of Genndy Tartakovsky and Avatar: The Last Air Bender of Michael Dante DiMartino & Bryan Konietzko.
Both series have been created as TV cartoon show in 4:3 screen, Samurai Jack is of Cartoon Network and Avatar The Last Airbender is of Nickelodeon. Both cartoon shows have a story inspired by Asian culture and mythology, as we can see them, but if in Samurai Jack there is only one main character with no character support, except other people who meets in every episode during his journey, in Avatar the main character Aang has two friends who travel with him helping him and later other characters will join him and help him, like one of the villain who will becomes good. Both type of animations are really good but they are also very different, even if both of them are 2D animated series. Genndy Tartakovsky uses a more simple animation with Flash, simple in the design of backgrounds and characters, even if you can see that there are a lot of original and interesting designs, with flat colours and a flat perspective. He uses less textures and less details. Even when characters interact with objects the animation continues to look bi-dimensional and few shadows are applied to objects and people, besides it is used more black than grey scale for the shadows, therefore when they are not well illuminated you only see a silhouette. Even if the animations of combat scenes in Samurai Jack are really fast and not so fluid, they are in cinematic scope, and we can see it from the cut of scenes and most of the time from the position of the camera, it is like to see an action-movie. In this animation show there is a continuous different use of the timing, from slow movements to quicker, with long moments of silence and no dialogues all based only on the facial expressions. You can see in this video an example of fighting scene with a good use of colours, actions and sounds.
In conclusion, these two animation shows are really different between them but still really good and I suggest to watch both.