One of the most fundamental aspects of Avatar is, trivially, its treatment of an Avatar. The protagonist remote operating a body not his, that, in short, of an avatar. It is evident that this theme is very similar to the Matrix, as explained here, although I would not talk about plagiarism.
A first consideration: the fact of having an avatar to be a whole narrative aspect to Bildungsroman in the sense that the protagonist describes his life learning the rules of his new reality. Here, in my opinion, this theme is played in more interesting than the Matrix View.
In Matrix, this element of the story is entirely within the protagonist is his awareness is not visible to the viewer. More specifically, almost visible to the viewer only to the extent that Neo becomes more adept at war with his opponents. From this point of view, it seems taken from a video game, and the element is quite divorced from narrative.
In addition, the two worlds in which the story takes place in the Matrix, do not interact much (at least in the first film, but in the other series), or at least interact only indirectly. This has the effect that the changes (seen in the Matrix) the main character, his maturity, has no reflection on his life from non-Avatar.
[Incidentally, this separation between the two worlds means that they are not exploited all the wonderful opportunities offered by recursive mechanisms within the narratives that possess different levels. An example: in the Matrix, the fantastic final scene where Jack Neytiri sees prejudice and while he is choking, would be simply impossible. As well as the betrayal theme (Cypher in The Matrix and symmetrically Trudy in Avatar), we may decline in the world of the Matrix in death the traitor, while in Avatar can be used to create a bridge between two worlds (which is only hinted at in the Matrix).]
Avatar
In contrast, the formation of the protagonist is seen by the viewer: in part in training Jack (and here the film is very similar to the Matrix, once again), and partly in its interaction with the world of aliens. In The Matrix, the symmetry is in relating to Neo with the Oracle, but this can only be understood in other films (and even then are a lot of logical errors, I think, but that's another story). In addition, the maturation (from Avatar) of the protagonist also has a flap on his life from non-Avatar, and this gives the narrative a tension that goes beyond the action itself.
summarize my opinion: in the Matrix, the interaction between the two worlds is small, and takes place at a purely confrontational. For this, it becomes almost an excuse to justify the action scenes. In Avatar, however, the interaction between the two worlds and the film, so they are taking up valuable potential use.
