Compete on aspects other than price.

If your product is truly better--there is one advantage you want to hold.

Make sure you have developed and designed an amazing first user experience. Sign up and user the competitors app--What sucks? What could be better? What wows you? Make the experience so good people want to pay you

Another good one, compete on service/support. It takes commitment but if products are very similar, the service and support can be presented as what you are really paying for.

Check their user forums/FAQ/Knowledge Base/GetSatisfaction, whatever they have, find out what current users gripes. wishes, and problems are. Use that intelligence in your product development and messaging/marketing.

Out. Hustle. Them.