How prestigious is an REPE internship at a small/medium shop?

PE firms like Blackstone primarily recruit from target schools or name brand companies. So while $4B is relatively good sized unless its a name that most people wouldn't need to use Google to find, it probably won't increase your "prestige". In RE there are shops that might have billions in AUM but its all in self storage, STNL, or something like that which doesn't draw headlines regularly. Unless you are well connected in MF PE circles, go to a target school, or come from a name brand shop, Blackstone/KKR/Starwood/etc will be unlikely without a stop or 2 first. Don't focus on prestige for the internship and worry about learning and being productive.