I had to pick Star Wars in this because they have more fan films several which are high quality. But I think Avatar can learn something from Star Wars in the fanon realm. The fanon writers and directors take what they are doing very seriously and when that level of commitment is seen in Avatar fanons (Distorted Reality, Legend of Genji, etc.) you see a much better outcome and product. I think even minor writers in Star Wars often take their minor projects to heart in that franchise.
Another difference that I think benefits Star Wars fanon is the amount of respect their fanbase has for it. I rarely see the good and even decent fanons being looked down on by fans. Star Wars fans often give well-made fanons more respect than official work. That is partially due to the mixed feelings about the Sequel Trilogy.