Definitely more selection and greater parity but economics often dictate decisions and the large state schools start with a leg up since their tuition etc are generally lower than a private schools.
Not for out-of-state students.
The out-of-state tuition at Maryland, Penn State, Ohio State etc. rival that of a major private schools.
It's silly to go to those state schools on the basis of academics alone - if you're not 'in-state'.