Anon is onto something here. I think what's key to understanding this dynamic of schizos vs pyschos is the normies' role in everything.
Pyschos dominate society, they are the ones you read about in your newspapers and in the history books. The great men of history were almost all psychopaths that knew how to play other humans (normies) to gain power and influence. A successful psychopath will amass tangible wealth and social recognition with relative ease, they will have the best chances of upwards economic mobility, and their names will be known and remembered, for better or for worse. The schizo's end game is typically isolation and self sufficiency as they focus on their own self/immediate surroundings, going largely unrecognized throughout the course of history.
This is true for even the more extreme psychopaths and schizos. Extreme psychopaths are the types most likely to be serial killers, and not only are they remembered by society, but they are typically glammorized for it. The extreme equivalent of schizophrenia is being a downtrodden nobody on the side of the road rambling to themselves or a lone wolf "terrorist" like Anthony Quinn Warner. Schizophrenia can be more debilitating.
Normies are enamored by psychopaths, just look at the culture of celebrity worship. The normies only see the psycho's wealth and outward successes, they then glorify them for these achievements and seek to emulate it or become associated with them out of a combination of admiration, direct manipulation, or envy. The psychopaths have the gift of gab, the ability to easily sell their visions to the normies, for they fear not of selling them self serving lies. The schizo, even if articulate and factual, simply can not have the same grip on the mainstream conscious, at least from what I've observed. You'd be hard pressed to identify major world leaders/elites in the last decade who lean more schizophrenic than psychopathic.
Perhaps it boils down to psychopaths being proactive and schizophrenics being reactive. Psychopaths can dominate the moment, but schizos can at least benefit from eventual hindsight potentially vindicating their claims, although that is often too little, too late. Psychopathic gaslighting is able to work just long enough for the psychopath to get what is needed out of a normie before disposing of them.
I genuinely believe that at their core psychopaths are evil creatures. Even if their psychopathic nature drives them towards something considered a net positive for humanity (for instance, philanthropy), there is this unshakable sin rooted in their motivation. The "anti-christ" will come in the form of a psychopath, not a schizophrenic.
Of course, we do see a similar sin manifest in schizos in the form of them believing themselves to be divine through direct intervention/communication with "god." What unifies the extreme ends of psychopaths and schizos is narcissism.