I don't think there is such thing as a "better school" because there is something for everyone at any school. For example, Oregon has the number one Landscape Architecture program in the country. So if you are looking for that, Oregon would be your place. I applied for that program and got in, but because it is a state school and I am from Florida, I didn't get much financial aid (got $10,000 out of $40,000). I also applied to Stanford but didn't get in (likely because I didn't get a 1500+ SAT).
Here's the thing. College is pretty much the same at all schools in terms of academic rigor. Obviously Harvard Law is going to differ from Arizona State, but a lot of the same things are learned at most large universities. The main difference is the type of people and culture. Having a high 1500 SAT says something about a kid. They are obviously going to be more disciplined and conscientious than a kid with a 1000 SAT. Don't get me wrong, I don't think any of that stuff matters, but the culture at a Stanford is much different than at a Oregon.
Stanford is in my opinion the best University in the WORLD. Elon Musk, Peter Thiel, Phil Knight, and so many more billionaires come from Stanford. It simply has the most resources and is located in a very special place (silicon valley). There is a reason why Grant Fisher, a kid with a 34 ACT, is struggling at Stanford.
So the short answer is that Stanford is "technically" the better school, but it really is up to the individual. I obviously would rather go to Oregon for the Landscape Architecture program.