Some of the answers seems to be predicated around prestigious school versus less prestigious school, but that doesn’t necessarily answer the question of big fish/small pond or small fish/big pond. There are a lot of prestigious schools out there that have high admissions standards, that may not be the ‘big pond’ it would seem to be (big pond meaning the kids there are these intellectual giant who will drive someone forward). Likewise, the school with seemingly ‘lower’ level of students might in fact be more a big pond intellectually, because the school seeks out kids who want knowledge, who enjoy learning, rather than spend their time gaming the admissions systems to get into a top level school…
In the end the real question itself comes down to what drives a student. Some kids need to be around others who are smarter than they are, better than they are, to give them motivation, other kids don’t care. I also will add, getting back to my original point, that when we say smarter/better, what do we mean? Is a school full of kids who have been focused their whole lives on getting into an elite school necessarily going to drive people forward? There are a lot of kids at elite universities and colleges who have little curiosity bout things outside their classes, for example, and that might be a turn off for some kids, whereas another school might be full of lot of diverse, interesting kids who help drive them forward, it all depends (and even at the schools famous for being a target destination as a name to go to, there are always a lot of bright, curious kids, too, along with the spawn of driven parents who aren’t curious about much).
This comes up all the time with music schools for performance degrees, about whether it is better to shoot for let’s say a Juilliard or similar level school, that probably would be more expensive, or take admission at a school where the typical student is not as strong musically, but where the kid might be able to get a good merit scholarship and have an excellent teacher…and it all comes down to the student, some get ‘driven up’ by being around top level students, others are perfectly fine as long as the teacher is good.
In terms of the big pond versus small pond (in terms of school size, not necessarily level) it depends on the kid as well, but my feeling always has been that a big school might be better, simply that because statistically, you might find other students you fit in with easier, because there is a larger pool. A kid might not do well at a small school where Greek life and sports dominate, where the kids are relatively homogeneous, if that is not their bent (on the other hand, there might be kids who love that kind of environment). If a kid is unsure, the larger school might be a better bet for a fit, simply because a large school tends to be an ocean of ponds of various sizes, rather than one ocean all the same.