Oh nickel, I can see you feel so cross and so down, and have for a long time felt rubbish about how your church is not growing but the other one is. it must feel really hard sometimes. Like niminy, I am not in the situation, but in my experience every church sets up stuff like FB pages and twitter feeds etc - I guess it's just the timing of it that was hard for you - that they did it straight after you did, and almost felt to you like an initiative that they nicked? Perhaps try to take it as a compliment - they thought what a great idea, and thought it would be a good thing to do to reach out to the town more.
It's not a competition, it can't be. As a church universal we're all about trying to grow and bring new people to faith, and some churches will use one style, some another, and it's good that there are different styles that reach different people. people will always need a church like yours, somewhere they feel they can celebrate in a more traditional manner. That's your USP as it were, and you're not trying to be something you're not. But the other church needs to be reaching out too - grow the kingdom, by any means and all, and a FB page is merely another way to help. And it's a good practical thing too for churches - for their existing members, to say what's on when etc.
I hope you can see that it can be a good thing for both places. I am really sorry you feel mocked and looked down on. Can you think of any examples of this, because this ought to be discussed with NV if so, becuase it is wrong and shouldn't be how a church operates.
Either way, I think we all need to find it in ourselves to be happy when a church is reaching out, in whatever way, and bringing new people to faith. :)
I'm sending love and prayers with this.