The stiff tulle is good for bunching up into areas of more solidity, like torsos or arms, while the really thin filmy stuff is good for draping, such as outer layers of shrouds. At JoAnn, you find a whole bunch of different weights and "hands" of that sort of fabric all in one section (the wedding dress section, more or less).
Warning: if you use a lot of the stiff kind, and not very much of the drapy kind, you stand a good chance of your ghost looking a lot like a wedding dress. If that's the effect you are going for, well, now you know how to get it. ;-)
And of course you can shred the edges and cut holes and tears in ithe tulle to make it more battered and scary looking. I like to keep any spare tulle wadded up in a tight ball, so it comes out wrinkly, which gives the ghost texture and interesting lighting effects under the black lights. But it never quite gets that organic stringiness that cheesecloth does when you distress it.