Competitions can be good for creating a little buzz around your company in the start up community and some of the judges or people in the audience could be potential investors. I did a bunch of college competitions as a part of a start up and we got validation, constructive feedback, and a little money out of it, which was great. We refined our pitch and were better prepared to answer the reoccurring questions and concerns we encountered. If you have the time for it, I would definitely recommend it.
I just did a quick search and found this
See what is applicable to you and go for it.