Fan art is a good test of skills - recreating the familiar, and an expression of appreciation I suppose. However, I put a high order of value on original material. Even original material based off of an existing franchise is far more preferable to me. I'm not saying there's a right or wrong about it, that's just my preference.
I'm a little divided on the subject. On the one hand, original artwork shows the artist's creativity and what they come up with on their own without much outside influence. They can imagine their own world and characters and put them in situations unique to their imagination and the world it came from. Further, if it's a very high quality piece of work,drawn to the last little detail (buckles, straps, zippers, hair, dirt, etc.) just makes it that much more enjoyable that they were able to come up with and put out a hard copy on their own. Fan work, on the other hand, has value to a person who really knows the characters and can get into the piece on a deeper level because they know background and can have a deeper connection to it. With fan work, you see a character or place that you know and can get excited about a new situation that their favorite characters are in. On top of that, a fan can also be awed at the amount of effort and detail put into a person that they know from watching, and the amount of detail that can be poured into the art that a cartoonist wouldn't be able to capture for the sake of the show still looking cartoony and the small time frame. All in all, both kinds of art can be mind-blowing, it's all about imagination and effort