In the comic books Flash (Barry Allen) dies and Wally takes over. In YJ, Flash is still alive, so wally hasn't taken over. Also, in Justice League Unlimited they're probably going by the comic books, YJ doesn't go by the comic books.
Young Justice is completely different from the comics and JLU. (JLU Is better in my opinion, because it is almost exactly like the comics, with a tad bit of animation flair and director imagination)
