Is it really identical? Try to look for differences and emphasise your unique selling points. It's rare there's only one way to spin a product and it's unrealistic to expect no competitors. I usually make a matrix of competitors against various attributes (e.g. price, features) and look for a gap.

For what it's worth, I've been on a project in a similar situation. The other project was packed with features and had tons of marketing. Our product had less features which might seem like a disadvantage but because of this we were able to make the UI much more focused, streamlined and uncluttered plus it was more robust which was important to some customers.