Both are excellent schools with a lot to offer and close in rankings. The rankings vary depending on which one you look at; overall they are close. I would only use rankings as one creteria as rankings can be misleading, You have two great schools to choose from so really you can’t make a bad decision.
Full disclosure; I am not an alum from either, however, I am from So Cal and part of the Trojan family. If you have been to SC I am sure you will agree that the campus is very nice; I think it’s beautiful and vibrant. ND is also beautiful and a very exciting place to be during football season with lots of traditions. I am sure you could have fun at either school.
I can’t comment about how well known USC or ND is in Europe. What I do know is, if you are interested in doing business in So Cal or Asia (Shinzo Abe, PM, Japan is alum), SC is very well known, respected and has a powerful alumni network. SC is a school on the rise and this year the addmission rate dropped to 16% so congrats to you for being accepted. BTW, SC is building a new university village and a new building for the business school. Both are going to be very impressive. SC has almost reached its goal for a recent capital campaign and receives generous gifts on an ongoing basis from alums like George Lucas.
All in all, life is good in So Cal and USC. Good luck and again, you can’t go wrong with either.