What you need to look at is the FBI Supplemental Homicide Report, this will tell you what you want to know. The current statistics are likely much the same as those laid out in this article from 2015:
https://www.washingtonpost.com/news/wonk/wp/2015/05/07/poison-is-a-womans-weapon/
From 1999-2012, we see that men committed 90% of all murders. Guns are used in the majority of all homicide cases. Men used guns 2/3 of the time and women used guns less than half the time.
If you take guns completely out of the equation and just look at all other methods of killing, you can see that men are more likely to beat someone to death with their own hands or with a blunt object, followed by strangling. Women are more likely to stab, asphyxiate, poison, or drown their victims. Keep in mind that a lot of women kill family members during domestic violence incidents (especially their children) - not strangers in a park. So I think it's difficult to draw any firm conclusion from this that applies to all circumstances. And, because men are responsible for so many more of the total murders that take place, more men will stab their victims to death overall, if that makes sense.
Regarding postmortem acts. Again, following the general trend outlined above, men are more likely to commit post-mortem acts (though we don't necessarily know that that disfiguration described by reports of the Janness case was specifically post-mortem, as in, the murderer hung around to do it - it could have been committed peri-mortem in a frenzy). Mutilation would likely be a signature act by the offender, something unnecessary to the actual commission of the crime but done for gratification purposes and related to the inner fantasy of the offender. It can substitute for sexual gratification IMO.
All opinions only.
