We want to be a part of YC and thinking of applying for W15 batch. Would it be a good idea? Is there a policy that prevents YC to accept companies in the same domain?
I would be prepared for the question "What do you understand about this that $COMPANY does not?", but you should expect them to ask that about the industry leader first, rather than about a startup with a market share measured in basis points, which describes the overwhelming majority of startups (YC funded or otherwise).
I would also be prepared to have people, perhaps including the YC folks and perhaps not, tell you "You're not actually in competition with them."
The companies who are our private beta customers have been using the other company's product (and a few others in the market) for long, and they were dissatisfied. We sat down with at least 15-20 of them and figured out what was the reason. We think we have "What do you understand about this that $COMPANY does not?" figured out. And the product has been very well received.
Actually, we ourselves think we are not in competition with them, because although we are trying to solve the same problem, our approach is starkly different from theirs. So, we're prepared for that as well. :)