Vandy’s faculty research quality is not as good as that in UW. Wake forest, Williams and Mary are not good research schools. Even Georgetown is not that great on research. All liberal arts colleges emphasize on teaching, not on research. So faculty research is not as good as that in flag ship state universities.
If you evaluate schools based on research output, of course, many state Us will be ahead.
Big state Us admit lots of students, their acceptance rates have to be high. Liberal arts schools are small, do not have many students as well as faculty members, more importantly, they do not have enough resources. If you know your field, you will notice that lots of them do not have all the databases in the library. In particular, in engineering, or business, liberal arts schools cannot compete due to cost.
Still, for undergraduate education, many liberal art schools are adequate. But for those truly exceptional, liberal arts schools might not be able to accommodate.
Big state Us have everything, but also more students to compete with. It is easy to get lost in a big state U. But for those who know what they want to do, and strive for it, big state U could be much better.