We have a Hario syphon at home. I've never used it (it's the girlfriend's baby) but I've watched her make plenty of coffee with it. There is always a little bit of water left in the bottom but I would say it is a lot less than half a cup.
Here is a video of the Hario in action (not my video) and you can see how much water is left in the bottom. I'm not familiar with the bodum syphon though.