If you are properly rooted in God, the presence of another ministry in the same vicinity will not affect your growth in any way. Have you seen a plant diminish because another was planted next to it? The forest is filled with trees. If you actually understand this it will help you.
God has designed it this way. Greater impact on the territory when things are clustered rather than isolated. This is the concept behind shopping malls, a cluster drives traffic. This is why you have financial districts, Silicon Valley; a cluster for tech companies. They have discovered how to create a cluster everyone grows.
It is the feeling of being threatened by the presence of another that diminishes. Fear drives away the blessing not the presence of another. The competitive spirit destroys the creative process within. Stay planted in what God called you to do, don’t copy and you’ll flourish.