I think the choice depends on the size of your stash and if you already have something that can be re-purposed and/or your budget If your stash can be folded, sorted by colour and fits in a dresser then this will work. If your stash is larger or you are the type that needs to see everything at once, then a cabinet works better.
My fabric and quilting stuff is stored in shopping bags and plastic bins until I can create a quilting area.