Working on a friend's house, we're installing a bathroom fan. He had planned to vent the fan out the closest soffit, which is only a few feet away. I'm trying to persuade him to vent it out the roof at best, or the side of the 2nd floor at worst, because I've always been told that you should go "up and out" with bathroom exhaust. What is the best method, and more importantly, why?
As far as I know, it doesn't really matter as long as it's vented outside. Venting into the attic is Very Bad -- in the winter, the humid air will condense and (if cold enough) freeze, and you'll effectively have water in the attic.
For any vents, the straighter the run is, the more efficient and quieter it is. Avoid corrugated pipes, and avoid bends and elbows as much as possible. For that reason, going into the soffit almost guarantees you'll have more bends than going through the roof.
As a DIY job, you'll also have to be sure you have the knowledge to cut a hole in the roof. I'd say it'd be far better to go out the side of the house (which is a bit easier to seal) than to go through the roof and cause a leak.