As for personal experiences: I once received an e-mail from a guy who favored our blog software over Wordpress because he liked our style. Since you didn't copy anyone but have a genuine product, chances are that people like your style better.
Now that there is competition, your initial idea for an app has been validated by another player which means your six months of work probably weren't wasted on a product no one would be interested in. See the competitor as a good sign.
If your idea is a good one, copycats would have jumped on the bandwagon eventually. You might think your head start would have give you some advantages (and it might have), but in this fast moving world it's probably only a minor factor.
I hope this makes sense.
I'm constantly downloading similar apps in bulk to compare/contrast, and I know I'm not alone. Put it out there and see what happens.
I wouldn't give up because someone else is working on what you are doing. Even if they have a similar product, you could target a different customer, or have a different business model.
Most apps don't have a winner-take-all approach. Try to figure out what you believe, and what differentiates your product.