I'm using "equal work" in an informal sense. (In the legal sense, yes, equal pay for equal work is the law, but also in the legal sense, you can't give an immigrant worker a green-card-path visa unless you can't find anyone in the States to do the same job, and we all know how creatively "the same job" gets defined.)
In the absence of strong evidence, I personally err on the side of caution.
I don't know what these mythical places are that vastly prefer men over women - every place I've ever worked at, everyone preferred people who are good at their job and are easy to get along with - mostly the easy to get along with part by the way.