Do they like hotdogs, mac and cheese? Then they will like the wienerschnitzel (sp?) My oldest is picky too but he always walks away full. And the entertainment will outshadow any food shortcomings--they will love getting out on the dance floor.
I am picky lol and we always go to biergarten every trip for lunch.I love the mac and cheese haha and the pretzel rolls and bread and they have some sort of chicken that I like from there.Your kids will like the food.
My picky DS ate NOTHING at Biergarten! We got him chicken nuggets at the McDonald's stand near Canada. I'm not a super picky eater, and the food at Biergarten is not my favorite, but I love the place for the entertainment and atmosphere.