Library school vs museum studies

I'm just starting to poke at the idea of going to grad school, and I'm trying to decide what to go for. Right now I have a part time job at a library (very part time), so obviously getting a MLIS couldn't hurt. But the org in charge is very hesitant to add new positions (and they have to be full-time, they won't do part-time positions any more, which everyone thinks is dumb, or I could just move up to a better part-time position and get tuition reimbursement). So if I want to look elsewhere, I could either still use the MLIS or go with the more interesting museum studies or even better, museum exhibition design. I really like that last one, because it meshes with the theatre tech work I also do. But MED is a pretty new field, and when I tried to talk to one of the local grad programs I got warned off because it's nonprofit and no one wants to do that. Way to sell me on your program.

But still -- so right now I'm looking at either in person at the Corcoran for the MED, or online for MLIS through U Wisc or UMD, or online for the Museum Studies through JHU. I can figure out the overlap between museum studies and museum exhibition design, but what I'm not sure about is how much overlap there is, generally, between library sciences and museum studies. Any specifics about any of those programs would be helpful, but I'd take general info, too.