Uh, I don't know if that's the difference between "public" and "private" as much as it is the difference between Texas and Arkansas. My cousin played for Evangel for a time during the "glory days" of their run from the mid 90s till their final year in 5A. Many a time I saw Evangel ruthlessly crush a ranked Texas 5A team.
Of course, in the 10-15 years since, we've seen the number and quality of Louisiana football decline, and elite private schools John Curtis and Evangel banished to lower classes in the name of "fairness"
while Texas has seen the rise of the "super-program" at the high school level, a new phenomenon. Don't get me wrong, Texas high school football has always been top notch. But the rise of Allen, Euless Trinity, Southlake Carroll, and the like have taken it to ridiculous levels. Programs from smaller states, even our absolute best, just can't hang. I've followed Trinity over the last decade, and seen them go from needing overtime to beat Evangel, to beating John Curtis by three touchdowns, and now they throttle the dominant superpower of Arkansas in a game that was never close and never in doubt. And I know for a fact that Don Shows and West Monroe want no part of that.
That is some kinda monster ya'll have built over there.