First, it solves the transfer problem of having to save files at home or at school. It's all online. Students can write in class, in the writing center, in the media center, at home, at the public library, and at Starbucks.
Since we have a campus license, I can set page-level access, so that everyone's draft is private. While all the tentative processes of rough composition take place writers can have their privacy (yet be visible to me for assessing their progress). When the first full rough cut is ready, I can open their pages to one peer mutually.
Moreover, I'm not collecting a variety of handwritten or typed drafts of intro paragraphs, counterarguments, supports and conclusions. All of their progress is not only visible but also documented as to when it was saved, thanks to a page history feature. I can see everyone's progress as soon as he or she clicks save. I can also gage each student's progress (or lack thereof) and add encouragement or warnings along the way.
Students report a few downsides. If they don't save frequently, they leave themselves open to power failures and lost keystrokes (PB Works has a save-and-continue feature in their Beta editor, coming). And they must have Internet access--not such a problem in this digital age, but still a factor for some that share their computers with family, or the power goes off (which did happen this year due some bad weather).
Still, the ability to work at school and at home in a common online medium has more pluses than minuses. Haven't we all heard the refrain "I can't write in class"? Indeed, some students are more productive at home, when they are alone and not hopping from one bell to the next. They can spread out their notes, sip coffee, and hunker down for some quality drafting. For instance, this year, in the week students were working our their first drafts, we had several snow days, and students could keep working away from school. And from home, I could watch their progress during our time away from school and offer coaching in the comment fields. The connectivity seemed to motivate both student and teacher, while helping everyone to beat cabin fever during the blizzard.
Next, I use Word to add my comments and mark the papers, send the amended file back through the wiki, and wait for the third and final draft.