Two women have fulfilled leadership roles in the UK during my lifetime.  Margaret Thatcher was widely resented by the political Left because she was willing to drive through controversial policies or pursue risky strategies, but ultimately proved more effective than most male leaders.  She was caricatured as 'swinging her handbag' to bludgeon her opponents in to line.  Her combative style evoked a mixed response from feminists, many of whom [at least secretly] admired her, even if they disagreed strongly with her ideology.

The current post-holder, Theresa May, lacks the sharp political acumen of her predecessor, but has displayed resolve in pushing through Cabinet and Parliament a highly divisive agenda concerning our relationship with the European Union.  She has attempted to engage with her [mostly male] opponents, both at home and in Europe, and I think it fair to say her style is more consensual and conciliatory than that of Mrs Thatcher, so "not talking to each other" is not down to refusal to negotiate on her part.  The verdict of history on her has yet to be reached.

Maybe having a better world is not a question about men or women but about honest people or unscrupulous people.

Are women more honest than men? It could be possible. Until now men did it not specially well. 

I heard that the only woman to have ruled China was the cruelest monarch in Chinese history. 

If women ruled the world, it would mean they'd be assertive and aggressive enough to wield power. It is unlikely that an average housewife would have authority in such a society.