The types of business ideas that will win is determined by who is doing the judging and what they are looking for. The winner will be selected based upon how well the idea is presented. Having lots of designs will be really important for events like Startup Weekend. Having a sound business idea will probably also be really important, but not as much. Having a functional prototype may even be less valuable than the other stuff.
Prototypes and Ideas
At hackathons a working demo may also be important, depending on the type of event and the judges. Some hackathons will only look at a demo. Even then, this can often be faked. Often times the judges may not be technically inclined. At codeathons your best bet is to focus on a solid business idea and present it well. At these types of events they want to see innovative ideas and they may not care if you don't have a product.
These types of events are great experiences for many reasons. The opportunity to network and meet like-minded folks can be invaluable. The chance to develop and refine your pitch can also be very rewarding. Having the chance to conceive of an idea, analyze the business opportunity, conduct user validation, and compete against the other participants, can be a wonderful learning experience.