I assume you're pretty tall, noob to snowboarding and riding NZ? You'd need to give more info about your stats, experience, riding style... then someone knowing the Genesis can chime in to estimate, if the binding could match your purpose. I haven't ridden the Genesis thus only general comments.
Equivalent is a wide term
Size (lenght) wise, yes. Expect the men's M to be a bit wider than the women's M. I'm all in to ride men's gear, IMO "women specific desing" is partly marketing blabla... However, a problem women could face with men's boots n bindings is that women - in general - have ower calf muscles thus women's boots have a different boot leg cut and women's bindings a lower highback in order to avoid pinching of the calf. I've tried some men's boots but the higher boot leg did pinch my calves; I've also tried several men's bindings and some work very well (the ones with rather low highback). Best would be to demo the binding with your boot to check, if the highback works for you.
Jones Flagship 158, Ride Farah 153, Jones Solution wmn 156, Rad Air Jewel 159.5, Jones Mothership 156
Ride Fame, Burton Escapade, Spark Afterburner
The average human has one breast and one testicle ~ Des McHale