Go for it. As another commenter said, it's called "competition". Coke/Pepsi, Ford/Chevy, etc.

Design your site to look better than his

If it's a paid app, you can beat him on price–or charge more and beat him on quality of features and service

Consider dropping one feature that he has, and adding one that he doesn't–even if it's trivial, it could help you differentiate.