Providence probably can open more doors academically than UConn. Except when you're in the engineering, pre-law, medicine, etc schools at UConn you're doing something right. But most basketball players don't pursue money-making/job-heavy majors.
Athletically, I believe UConn can open more doors than PC simply based off of history and prestige. You rarely see centers/big-men get drafted from smaller conferences and schools. Sure it happens, but they need to make a huge run in the NCAAT to get exposure and play better competition.