It depends a lot on what your field is. I'm in the humanities, and taking an unfunded offer would not be a good idea because the job market is rather dismal. Like others have said, only go into debt if you know for sure that you'll be able to pay it back quickly.
If you do end up going to the lesser known school with funding, there may be other ways to make a name for yourself (conferences, publications), but again this will depend on your field. Best of luck!