I like Avengers because it's a fun show. Sure, the show draws heavily from plots of recent years, but that's not necessarily a bad thing. I'm sure DC would draw from that stuff as well if their events weren't Infinite Crisis, Infiniter Crisis, The Infinitest Crisis of Finality and whatnot. However, it's definitely skewed toward a younger audience and with the exception of Hank Pym (and maybe the Hulk), there's very little character growth.
I like Young Justice too. The YJ world feels a lot deeper than Avengers, partially because they often pan out to what the rest of the world is up to in an episode. The Avengers isn't a Marvel Universe show in the same way that Young Justice is, because it's specifically geared towards one team and really only hints at using the bigger world. That looks to be changing in season two, with appearances of the Fantastic Four, Heroes for Hire and the Guardians of the Galaxy in the first five episodes, but I'd still be inclined to give the edge to YJ so far.
Avengers does have the bigger villains and uses them as more of a threat than YJ. Villains such as the Joker or Black Adam shouldn't be pushed aside in favor of Sportsmaster. Psimon shouldn't be able to take out the entire Justice League, but Joker gets taken down handily after making five lines of dialogue.
All in all, both shows are good. They both have flaws but so do most children cartoons.