Should I apply to YC if my site is similar to a previous YC site?

I'm currently working on a neat project. My co-founder and I have started the YC application for this semester. We got to the question about our competitors and mentioned one that we're aware of - it's a recent YC service (MessageParty).

Yes, we're in the exact same market and yes the concepts are very similar. We obviously feel like ours is great and are passionate about it. We like the concept of MessageParty, too, but it's not how we would have done it. It's not how we're doing ours.

Should we still apply to YCombinator? We lost of good amount of steam at this question, and decided to save the application and come back to it tomorrow. We were getting into the "what ifs" and stuff. We concluded with the agreement that we're going to go through with the application and just see how it goes. It's an experience either way - one that I've wanted to do for the past two years.