Both. Neither. It's complicated.
Let's break it down using cis women as an example.
Body: If a "female" body is what makes a woman, then do women who have had double mastectomies cease to be women? No. Who have their hair cut short or shaved completely? No. Who have small hips and broad shoulders? No.
Genitals: If genitals make a woman, then do women who have had full or partial hysterectomies cease to be women? No. Who have had vaginectomies? No.
Hormones: If hormones make a woman, then do women who are menopausal cease to be women? No. Who experience other hormone imbalances? No.
Motherhood: If a the ability to be a mother is what makes a woman, then what about those who are infertile or otherwise cannot get pregnant or carry to term? Still women.
Social role: If social role is what makes a woman, then do those who are breadwinners, work in male-dominated or traditionally "masculine" fields cease to be women? Nope. What about those who are in relationships with other women so that it renders speculations about who is the "man" and the "woman" in the relationship meaningless? Still women!
Clothes: If clothing and presentation makes a woman, then do those who have never worn a dress in their life cease to be women? Those who wear suits and shop in the men's section cease to be women? Those who don't wear makeup? Not a chance!
Relationships: If a woman gets along with men better and has few, if any, female friends, does she cease to be a woman? If she prefers being the pursuer in dating, the top in the bedroom... I think you all know the answer.

I think questions like this are interesting, but ultimately useless and unhelpful. We shouldn't be focusing on what criteria someone might need to meet in order to be allowed to identify and live as a gender, we should be talking about ways to break down those barriers so that more people can get the medical and mental heath care that they need so that they can start living as the person that they feel that they are. Doing this will also help out our nonbinary and other gendered siblings as well, who don't currently have access to the same social infrastructure to call upon that trans* men and women do for the purposes of transitioning and being recognized. Sure, it'll remove some of the shorthand cues and symbols that MtFs and FtMs find so helpful, but those cultural assumptions usually do more harm than good.