I find these arguments strange and unnecessary. It’s hard to compare numbers when you’re looking at schools of completely different sizes. Rice has about 900 faculty members for it’s 7,000 students. In addition, different schools are known for different things. Rice is particularly strong in music, architecture and STEM fields to name a few. They also have a highly rated Sports Management major - go figure. Their pre-meds end up at great medical schools. But you can’t compare medical schools themselves since Rice doesn’t have an MD program of their own. They are not ranked as high in some other areas but I would say most of the kids who choose Rice choose it for the fit. Just like many kids choose strong Liberal Arts colleges because of the unique opportunities offered based on their wants and needs. I wouldn’t suggest their education is lesser because they maybe don’t have access to as strong of an engineering program as Michigan.
OP wanted to know if Rice is considered as prestigious as other T20 schools. In my opinion, it’s ranked high for many reasons, but I guess it just depends on whether or not those reasons are important to you!