Being privately funded, they have much higher chance of satisfying obscure customer request. Once companies are loaded with VC funds, they generally focus towards 'big-picture' features etc to impress the board members, VC's.
So even if the smaller company fills more obscure gaps at first the bigger company will continue to gain steam and continue to need growth. That need for growth will eventually lead them back around to the obscure customers once they’ve gained all the mainstream customers they think they can. When that happens the company with the VC money will have grown much larger than the private company and will be able to put more resources into getting those obscure customers.
In my case Google (the ultimate example of a company that grew off VC money) actually sent a representative out to our company to sell us on Google Docs. Having the money to send someone out to an obscure little agency like mine is exactly what I mean by “more resources”