I know there is no general answer to this question, that it depends on the person. Having said that, my experiences with women are way messier than those with men. I was so brutally flirted with, and than when I showed genuine interest in hooking up, had them back out. I had a girl invite me to her room to sleep with her (more than once), she was not sober, though, and the time I was willing to accept her invitation, her friend showed up and messed my plans. And when I told her I'd like to kiss her the next evening, she was surprised, shocked even. WTF?! I even managed to hook up with the narcissistic stalkery girl. Luckily it didn't last long, I ended it in time, and there was no real damage. I know that these are my individual experiences and not the general rule, but these things never happened to me with men. I think women are so much more complicated and messy than men.
I didn't have a lot of partners, neither sexual nor romantic ones. Since I came out, I dated women exclusively. I lost interest in men. Now I am single for some time now and I haven't had sex in almost six months and I am starting to miss it really hard. I even started thinking about men sexually. I think that the loneliness and too long abstinence have something to do with it. If I would find a man really attractive and have a chance to have sex with him, I wouldn't refuse it, I guess. But when a guy hits on me seriously, I am not really interested. I just find women so much more interested and attractive. I feel for women what I never did for men, neither in the range of emotions or in intensity.
I said a few times, if I would know that I could feel complete with a man, I would forgo women instantly and focus on men. But I feel that I would always miss being with a woman. And I don't want to turn to men out of despair, I think that it can lead to a bad path. But women seem to be driving me crazy the way the men never did. And yet, I want a woman!