I will add that there are a few very well recognized small private universities. These can be great if you don't really know what you want to do and plan on going and figuring it out while there.
Ex. A degree in engineering from Pepperdine may sound more distinguished than a degree in engineering from Cal Poly SLO if someone doesn't know about engineering. Even though SLO has one of the top programs in the US for engineering and Pepperdine is unranked as far as I know.
However, if this private university has a 50% acceptance rate (that's quite high) then it may not be in that prestigious small university category, (but you didn't name it, so I could be wrong).
I guess it's about who you want to impress, if it is a prestigious small university, then do you want to impress the general public with that name, or the people in your field with cum laude in the ranked program?