A reviewer I respect gave Batman Begins an A, so... I wanted to know if the movie would be appropriate for two kids, 7 & 10, and where the PG-13 rating came from.
7 is too young. It was quite violent and very intense. The scene where his parents are killed...
However, I can't remember a single profanity, there was no nudity or inappropriate moral behavior, and Batman didn't kill anyone. But there was a lot of violence.
10 years old might be ok. I would recommend waiting until it's on DVD and renting it, after you preview it; it'll be much less intense for a kid at home.