My instinct is to say a proper psychopath would manage things better than your ex, Lion, but plenty of people with anti-social personality disorder do live chaotically. I guess it depends on their particular collection of traits/characteristics.
The word 'psychopath' is currently out of favour with mental health professionals, who mostly prefer 'anti-social personality disorder'. There is intense disagreement over this, and even over whether psychopathy is a PD or a different kind of neurological phenomenon.
A personality disorder is a very rigid personality. NT people move between different states all the time: we're sometimes narcissistic; sometimes cruel; sometimes dependent, and all the rest. It's normal to be in several different states over the course of a day and to be feeling two or three different things at the same time. NT people take this for granted and have freedom to choose whether to go with one state for now or change our attitude. Personality disordered people do not have this range and lack the freedom to choose; they're locked in their personal patterns and cannot understand that other people's characters are more fluid.
When the current DSM (v5) was being written, the panel was in favour of completely altering the Cluster B structure. All of the disorders were going to be called 'sociopathy' (it means to have pathological difficulties with society) and the various characteristics - anti-social, histrionic, narcissistic, borderline and others - would be classified as traits. This would give professionals the capacity to describe each individual's disorder in terms that applied particularly to them. There was much opposition to this (entertainingly, a lot of it came from people with NPD guarding their label!) so what we have at the moment is a sort of compromise; it's used differently by different schools of psychiatry although the fundamental move towards diagnosing multiple traits has been welcomed.
All of which is a long-winded way of saying don't get too hung up on the labels. If you are dealing with someone who "is not as others" and seems terribly inflexible in their thinking, then knowing about the traits can help you decide how to deal with them. If calling it sociopathy, ASPD, NPD, or whatever helps you understand and classify it, then use the words you find helpful. Ignore people who try to say you mustn't unless there's a clinical diagnosis - the majority of Cluster B subjects never present for diagnosis and, even if they do, a different shrink might use different words for the same thing.