I think the majority of medical schools are privatized, though the ratio is probably larger for DO schools. But anyway, the reason why the majority of DO schools are private is explained through their history, recent trends, and aims. But anyway, the notion that privates are harder to get into than publics isn't a true one, save for the top 10-15 schools ( JHU, WashU, Harvard, and including a public UCLA) most schools are about equally competitive and at times it's probably more likely that a public MD school might be more competitive than a Private MD school since many are lower tier as compared to state schools being generally mid tier and for in-state students incredibly cheaper.