You shouldn't worry about things you can't control. To a degree, ignorance is bliss. You can't know whether or not your competitor screws up in the future. You can't know whether you screw up in the future. You can just do your best. The goal is to stay focused and motivated. (Who would have thought). ;-)

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.