Neither is the absolute better or worse option for every possible student.
The biggest difference is the settings. UA will have about 35K (ugrad + grad) students on a massive campus, while UR has less than 3500 on a smaller more intimate campus. UA will have a combination of students in all sorts of academic and SES ranges, while UR will have mostly higher-stats students from wealthy families. UA is deep south, while UR is southern but of a different flavor. UA has massive sporting arenas/stadiums and competes in major colleges sports conferences, while UR has a different sort of Rah Rah enthusiasm and participates in smaller arenas against less obsessed rivals.
If you plan to study hard and do your best, I don’t think it will matter for your professional career. There is a possibility that you will find more personal happiness at one over the other - and that personal happiness may be more conducive for academic success, which may end up leading to more success after graduation.
None of us can tell you which is a better fit for your personal happiness. Some students would find their space on either campus. Other students would definitely be happier at one over the other. You should do more research to figure out if you have a preference, or if you could thrive at either.