The only one that can compete is the few lucky percent at top that have health and strength to do so. Manning up is not an achievement, it is a symptom of the core issue in cultural differences in how women and men are treated.
The general cultural view seen in for example health care is that men are assumed healthy and strong. This is great if you are that, but catastrophic if you aren't. Treatments get delayed, problems worsened, and in psychology there is a recognized problem of not seeing mental illness in men. For women its not perfect either. While assumed poor health do generally lead to faster treatment and better contact with the health care for women, the doctors don't believe in actually curing problems so health care for women has disproportionation amount of only addressing symptoms. In averages, some treatment is still better than no treatment which is reflected in the statistics and increased life span.
This pattern show up all the time in gender studies. Men end up as majority at the top and bottom of the charts, women at the middle. The fact that you are a woman should in average give you an advantage at work in comparison to men with same health issues, pushing you towards the middle. Men can pretend and hide the health issue for a while (ie manning up), but its unlikely to work and carries with it some major health risks, not to mention that shitastic experience. In all its a bad situation for everyone with health issues, regardless of gender.