The Hunger Games has a more general/universal appeal. It's not just marketed for young tween girls, it also appeals to a lot of young-adults, especially males. And I don't know if it's just me, but while watching the HG, it didn't feel like I was watching a 'Hollywood' movie at all. It felt like a full fledged film, those worthy of Oscars.
Long story short, I don't think it's stealing the thunder away from Twilight. The public lost interest in Twilight because of its own flaws.