I have yet to submit a game for Steam Greenlight, so forgive me if my perspective is not the one you're looking for. However, I've worked on a variety of fan projects through the design process, have researched this a lot, and am preparing to release a game, so I can speak to a bit of experience on the subject.
In general, I tend to think public demos are not necessarily the most strategic.
has a good perspective on the subject. It might interest people to play the game, but may already give them their "fill" of it. In contrast, trailers and screenshots generate interest while giving them a bit of a hunger for actually playing it.
However, I think that private demos are extremely valuable, especially early in development. If you have an idea and early process for a game, private testing in that stage can help redirect the rest of the design if people report issues, give you a general feel for the game's strengths, and also be a good source of motivation. Assembling 3-10 people to test an early version of the game can give great feedback while avoiding potential revenue loss that'd accompany a public demo release.