comics: Avengers > JLA (more of a gut general enjoyment rather than deep analysis of eras, many of which I probably haven't even read at this point)
cartoons: JLA > Avengers (years of fond memories of Superfriends and Timm-era JLA 'toons trumps the 90s Saban-produced Avengers debacle and the cool Avengers EMH toon which nonetheless clearly took cues from the Justice League show)
movies: Avengers > JLA (yeah, I know there's been no JLA movie yet; but IMO, DC/WB has had no excuse for decades not to try)
overall, Avengers > JLA