Competition is important as it brings the best to the top.
If you feel threatened then ask yourself why.
Then
Answer the challenge.
I've got a club night when Julie Feelthis is in town.
They must be daft, did they just not look around, or, are they threatening me?
I dont care because I know that I've got a good show too that night and so far every night has been a good night.
Confidence in your product.