What we used to have is this: choice.
Here there are both gov paid public and private owned education institutions that go from preeschool up to the higher tier.
There's a handful of carreers that are only found in either one or the other, like medicine wich is only taught in public universities.
Now, how it worked?
Public university: Regardless of you graduating either from a public or private high school, you needed to have really good grades to be automatically acepted on a public university. Each public institution would have a freshman quota for each career. Just before graduating highschool everyone did a vocational test, followed by an academic test in which among other things you could select 3 carrers in up to 3 different public universities.
If your average grades were spotless and your aptitude test was really good too you could get accepted automatically. That's it, if yoy were above the cut out from the quota. Oh also this quota had something like 60% graduates from public highschool and 40% from private ones.
This above only was to fill up a certain ammount of students all which invariably were exceptional academically.
The rest of the freshman quota was filled generally through internal admision tests. I entered this way, ranking 32 among 3000 applicants for that career (electronic engineering). Only the top 60 were acepted that year.
If you failed enough classes or lost two semesters in a row (some unis had slight different rules). You were out and needed to reapply the next year or banned for x ammount of semesters or forver, again, some had different rules.
You had to pay what was basically token payments mosly to cover part of the administration expenses but also most equipment (generally books and a scientific calculator) were on you. You could borrow books on a library but not take them out so most people just bougth photocopies of them ( copyrigths be dam).
Private universities: You showed up with the money and papers and that's it. Of course, you also needed to have the luck of having an open spot for the carreer, whoever if enough people was trying to enter the same career that was already filled they simply opened up another slot for a new batch of students, hired another few teachers or assigned extra classes to the ones already working and that was it. There were ranges on prices some were ultra expensive, others were midlly expensive, others were really cheap comparatively but still expensive. In some private universities if you managed to have perfect or almost perfect grades you could ask for a partial or total grant.
I ended up graduating as a tech from one of this as I needed to work and the public uni really didn't allowed you the time or flexibility to accommodate your scheduled around workhours.