You can absolutely find motivated peers and professors at state schools, particularly if you look at places like the honors college. If you want to land a good job, go to a good grad school, etc (which is the goal for most people), all of that is 100% possible from a state school.
However, if you want to do something non-traditional (startups, research abroad, "choose your own adventure" style careers), I found that the "elite" school offered a lot more opportunity. Part of that is due to funding/size, where top schools have more money to allocate to students who ask for it. Students at elite schools have more support on average (from family as well as the school itself), so they tend to have more opportunities open, earlier.
It's like the difference between a big city and a small town. Plenty of people are successful without living in a huge city, so it's definitely possible. You could argue that the average drive of folks in a big city is higher, but a lot of that has to do with resources and opportunities as well.
The top students at a good state school would absolutely fit in at an elite school. The only difference I saw was in the support/resources they had before coming to college.