Its pretty well understood that p/p schools do have advantages over public schools, which is why parents that are able to offer these opportunities to their children send them there as opposed to public schools. These kids, in most cases, have excellent family support and the opportunities to flourish in safer, more structured environments. If there were no advantages, parents wouldn't send their kids there. This translates to the football field.
A better question in my eyes is what makes the public schools that are traditionally successful, competitive most years. Small schools will always have ebbs and flows in talent, class sizes etc. What do Adams Central, Linton Stockton, North Judson, Pioneer, Webo, Sheridan, Eastbrook, etc do that make them successful consistently??? Is it weight room dedication, culture, coaching, game philosophy, youth programs?
I've always been of the mindset if you don't like losing get better. Trying to make a universal system of equity isn't going to happen, nor should it in my opinion, so go out and work harder/ coach better. Build up your regular season schedule to prep for the tournament, stretch your teams in summer scrimmages, participate in 7 on 7's and most importantly get your kids competing in the offseason (track, wrestling, basketball, etc)!