I think women generally or extroverted men specifically are underdiagnosed. The gender ratio is getting lower every study (now 1:3?). Similar what Issy said, my ASD-like grandmother was institutionalized while my ASD-like grandfather was celebrated as the eccentric scientist. It may be that he fit the ASD stereotype better and might have been DX'd, while she was "crazy". Otherwise, the ASD gene appears to have gone down the female line in my family (mother, me, niece, daughter), although my therapist swears my son has the "female" presentation (and so can't get diagnosed). In my family being male means less likely to exhibit Autistic characteristics given the current definition (severe social impairment).
Putting that aside ---- if the question is whether to be an Autistic man or NT woman... in the Corporate workplaces I have known, Autistic men can achieve greater pay and workplace success than most women (NT or ASD). In the household, I see Autistic men or NT woman fairing well or not based on adherence or not to cultural norms (many are hurtful). Of course in different cultures it may be balanced (which ones?! I'll move). Being an ASD woman has benefits (I have coached my Allistic husband to buck gender norms and establish a good household for our 2e children, I have achieved more in the workplace than most NT females) and liabilities (I have not achieved the same workplace success as my ASD male peers, the "double duty" of work and childcare that women are subject to is especially painful). I would try to do my best in whatever gender or social role or diagnosis. It's annoying to have limitations, physical or social, whether by neurotype, gender or all types of human differences.