So far you haven't explained how you're different from the competitor. If there's nothing, then you have a problem anyway.
If you do have a nice competitive advantage, your argument is that the market is certainly large enough for many players, and their existence will only increase the awareness of the root problem and that there are tools to solve it.
Typical advantages are:
- more experienced team (although sounds like you don't have this)
- celebrity status (although it sounds like they have it)
- new perspective / story (maybe you can win here)
- better business model (you're making money while they're "figuring it out")
- traction (customers actually paying you money for it)
If you can't find an advantage, you might consider proceeding without funding. If you have even mild traction you might have a better story, or you might be able to get "bought" by that other company (read: great job with signing bonus and stock options that have a chance at being worth something).