They’re peer schools for both academics and professional opportunities, but have a different atmosphere.
Notre Dame is definitely a Catholic school. 80% students are Catholic and, while not all are practicing and observant, you won’t find many atheists and agnostics. There’s a strong core curriculum; you’ll have to take 2 each of Religion/Theology, Philosophy, Mathematics, Science, and physical education, plus one History, one social science, and one either art or literature (13). Overall, the students are both involved in spectator sports (expect far-reaching enthusiasm for the football team) and practice sports themselves, often being former high school varsity athletes. Politically, the campus is conservative as far as colleges go and is considered the most conservative of the “big” Catholic colleges (with BC, Georgetown, and Holy Cross), although not “conservative catholic” doctrinally. THe alumni network is very strong in the Midwest and on the East Coast. It’s in a rural location but there’s plenty going on on campus so you shouldn’t fear getting bored! Weather-wise, the winters are rather cold and snowy but you have four distinct seasons.
USC has a very different atmosphere. It’s definitely SoCal in vibe. There’s a bit more variety for top majors: Students are aspiring journalists, film-makers, script-writers, as well as engineers and entrepreneurs. It’s in LA and the neighborhood isn’t good, although the school employs lots of people to ensure the students are safe on campus and off campus in a roughly 2-mile radius. But at the same time, you have LA at your fingertips! Politically it’s more liberal than Notre Dame, and it’s not religious. As for the requirements, you don’t have history, philosophy, or religion required; you have to take one class on Western Civ, one class on Global Cultures, one each of Scientific Inquiry, Scientific approaches, writing, Diversity, social issues, and arts/letters (8). You won’t have seasons - pretty much it’ll either be warm and sunny, or hot and sunny.