I'll back this up a bit... who came first on the web? You or the competitor?
You can both sell the same thing, but which site has more traction/longevity? New kids on the block, for example, must have more pizazz than the original. And if doing the same thing might suffer the same way that Hollowood (sic) movie sequels do... where the sequel does not do any where near as well as the original.
Forget the analogies above. What you should concentrate on is delivering a better user experience than your competitors. Period.
And to figure out how to do that, you'll have to invest in marketing tests.
Look that up and go from there.