Agreed that there’s a lot of applicant-pool overlap between WashU and Rice. I think Rice also has a fair amount of overlap with schools that have “nerdier” reputations, like UChicago and Harvey Mudd. While WashU is obviously highly academic, I think it has a more mainstream social vibe, whereas Rice kind of straddles mainstream and nerdy, if that makes sense. That’s my impression, anyway.
Rice is also a great baseball school, although I’m still unclear as to whether there’s walk-on potential for this student at D1’s like Rice or only at the D3 schools. Sports fandom in general is relatively subdued for a D1 school, but baseball has historically been their strongest sport.