If possible, visit both schools and spend as much time on campus as you can attending classes, spending a night in the dorms, etc. Rice offers overnight visits for seniors. https://riceadmission.rice.edu/portal/visit-overnight
For the class of 2022, Brown filled 44.3 percent of its class with ED applicants. Rice filled about a third of its class with ED applicants. If you like both schools equally well, the odds would say ED at Brown. If not admitted at Brown ED, then RD at Rice. Rice offers some merit scholarship as well as meeting full financial need. If Rice is the best fit for you, and if they both are affordable, follow your heart.