A recent discussion on this at my work was centred around the notion that large phones don't generally fit in women's clothes pockets (when they have pockets), as the pockets tend to be smaller. There seems to be an inherent sexism in phone design (and clothing design, and many other things).
I've been mostly wearing men's pants for the past few years to get past the pocket problem (skinny leg men's pants fit me pretty well and still have OK pockets). I'm probably in the minority though, most women just carry a pocketbook.
That is very culture dependent, I think. I don’t know a single woman who usually carries a purse! (I live in Norway. And maybe my acquaintances are unusual. But still.)