I can’t say anything about Austin, but I was accepted on scholarship to USC, and am currently attending Michigan.
People: Nicer looking people at USC, Nicer people at Michigan (you’ll be fairly surprised how nice Midwesterners are relative to the people you usually encounter in California).
Facilities: the USC is incredibly beautiful (Disneyland vibe). Michigan is more ordinary college town looking, with the exceptions of the Ross business school and Law School - both of those are gorgeous. Both colleges will give you more resources than you can handle, but USC will be more likely to spoon feed it to you because of the smaller size of the campus.
Academics: people at Michigan are smarter. I visited both schools for different programs and sat in on classes. From talking to a friend who goes to USC right now, the only reason USC has higher standardized test scores is because of it’s sizable international population with very smart students pulling the averages up. In your case, Michigan also has the better ranked engineering school.
Sports: it’s a wash. Both campuses are incredible and go hard with tailgates on game day. Both have their legendary rivals.
Resources: Tie. Both schools have advantages over each other. USC has LA, and it’s location in Cali serves as a ticket to the International trade routes of the Pacific (I’m a business major lol), so it’s extremely useful for if you plan on anything internationally related. Michigan has the bigger pure endowment in terms of money, and a better alumni network - it’s more spread out nationally and larger than that of the West coast focused Trojan family
Nightlife: Parties are everywhere at USC. You actually can’t avoid them if you tried. Michigan has a stuff going on al the time too, but because of the larger size, you can choose to avoid the parties whenever you want. USC is 3 minutes south of downtown LA, while Michigan has Ann arbor bars and clubs.
Weather: Cali will be much nicer. Michigan can get outright dreary looking during the winter. However, you will adapt MUCH faster than you’d think - I have several Cali friends who agree with this.
Feel free to ask for more info; just thought I’d help by providing personal insight!