Philosophically, Boeing have had a long time to learn from "tombstone technology", Airbus are relative newcomers, but they'll learn from their mistakes just as well as Boeing have.
Fact of the matter is, when you strap your rear end to the airplane, it doesn't matter whether it's been built by Boeing, Airbus or your local kit-builder, you stop worrying about who built it and start hoping it gets where you are going intact. If you fly either of the big two your chances are pretty good!