I know this has been posted already, but I think it was Barnett for both movies just because it is the exact same classroom in both films.
However, if I'm not mistaken, in the "From Star Wars to Indiana Jones: The Best of the Lucasfilm Archive" book, the model miniatures for the set designers are labeled differently for both movies. The "Raiders" classroom has a Barnett label, while "Last Crusade" has a Marshall label. I'm at work and away from my bookcase, so I can't verify this right now, but if someone has the book reletively handy, they can confirm this for me.
Regardless, I'm still convinced they were the same college. But, then again, until I discovered these fansites back in February, I still thought Indy taught at Princeton in "Raiders" and "LC". Of course, I was basing this on the "Young Indiana Jones Chronicles" and the fact that his father taught there in the series, and the campus looked so similar to the one from the movies. But that's just me, I'm just that type of cat.