I have been in relationships with both men and women, all NTs, and have found it much harder to communicate with women. Based solely on my personal experiences, the women I was with were more sensitive than the men - quick to get defensive, had more emotionally based reactions, and most tried to avoid conflict of any kind, which led to Aspie things I did just building up under their skin until (sometimes months later) they would explode in a rage. As has been mentioned by many of you, I had no idea my girlfriends had even been experiencing any problems with my behavior or something I had said that didn’t sit well with them. It was as if I was supposed to read their minds to determine what was bothering them.
Also, I found women to be more needy and suffocating. From what I understand, they weren’t really needy from an NT perspective, but they were for me. I need serious hermit time, sometimes preferring not to see or speak to anyone for days, and although I was very clear with them from the beginning that I was a loner, they seemed to think they could change me and they would grow frustrated, angry, and despondent when I didn’t.
They were also more social than the men. Well, maybe not necessarily more social, as two were introverts, but they wanted me to attend all of their family functions or go out with their friends, and would get irritated with me when I declined, whereas the guys who were extraverts didn’t care whether I went or not.
Others have already posted some excellent advice for communicating. I would only add that if you want to pursue a relationship with an NT woman, I recommend that if you see a woman a few times and feel you want to take it to the next level, be upfront that you have ASD, as that can assist her in discovering more about it, which might make her more patient and not apt to take things too personally. Also, when the going gets tough, as it likely will, find books or a neurodiverse couples counselor who can assist you in communicating with each other. (I was diagnosed only a couple of years ago, so I didn’t have a clue as to why I felt different from everyone I had ever dated, and didn’t have the opportunity to take advantage of those resources while in those relationships.)