About Lawrenceville, I know some people there who definitely aren't over-sophisticated and who didn't grow up too fast, but I know there are a group of girls there who do (like most schools).
That being said, why "should" you go to Andover? Is it for the name? You can't go somewhere just for the name, and remember this. Among normal human beings, Andover is definitely more prestigious. However, among colleges (and possibly workplaces after college) I'm sure neither is more "prestigious" than the other.