The social and party atmosphere at ND is quite active but much of the ND experience has to do with the residential system, participating in sports and enjoying the school spirit. Not just getting drunk. The school is too demanding for that.
ND is a true undergraduate residential campus while USC is certainly not that. 67% of USC students live off campus. Only 33% are in USC college housing. Almost all ND students affilliate with their residence all 4 years. One or two are actually called colleges.
The other difference is endowment. ND has roughly $1 million per student while USC has roughly $100,000. If you visit the campuses you can tell the difference.
It would be impossible to say they are peer schools. USC has 45,000 students, 45% undergraduate. ND has 11,000, 72% undergraduate.