But is the threat lower? It's lower because women take steps to avoid certain times and places, and this means that the statistics on how often men and women are victims of assault are already based on that mitigation behaviour by women. And it's the actual statistical frequencies of becoming an assault victim which then are used define the threat level we are talking about here.
So the two are intertwined: The risk is lower for women because women are already taking more precautions.
What would happen if women took all the same risks men do? Which sex would face a higher threat of being assaulted?
I suspect it would be women, because of the average strength differences (someone planning an attack prefers victims who can't fight back as effectively), and because women would face risks of attack for more reason than most men: not just muggings, say, or gang fights etc. but sexual assault as well.
It's difficult to draw conclusions about risk taking preferences given all this, because absent the mitigating behaviour many women engage in, the risk of attack would probably be higher for women than for men.