Please read https://www.brown.edu/academics/neuroscience/undergraduate/neuroscience-concentration-requirements for Brown’s Neuroscience graduation requirement. Neuroscience is one of the best departments in Brown, better than neuroscience programs in other Ivies in my opinion. Rice’s Neuroscience program is housed in the BioSciences Department.
Students in both schools love their schools. Read http://talk.collegeconfidential.com/discussion/comment/21697716/#Comment_21697716
Watch https://www.youtube.com/watch?v=pxCQwGcZGpk .
For applicant numbers from both schools, read https://www.aamc.org/download/321456/data/factstablea2-6.pdf
Please note that although Rice has fewer students per class, Rice (29%) has more Asian students per class than Brown (14%).
Best luck to your application. ;