I'm not sufficiently familiar with Egyptian grooming preferences to address the latter part of your question, but there is a straightforward answer to the first part of the query. Hatshepsut was ruling Egypt, while Nefertiti was the pharaoh's consort, and was not. (There has been some speculation that Nefertiti did reign briefly as pharaoh after Akhenaten's death, but this is disputed and we have no images of her that unequivocally show her as pharaoh).

We have no chronicles or collections of royal documents that go back to c.1500 BCE, so the questions of why Hatshepsut did as she did, and how her subjects' attitudes to her rule were affected by her gender, are essentially unanswerable – we have to extrapolate what we can from surviving monuments and the representations on them (which in Hatshepsut's case were, famously, largely destroyed by her stepson and immediate successor). But with the exception of one ruler who took over the throne at a time of national crisis, she was the first female pharaoh, and it is commonly assumed that it was necessary for her to stress her suitability for the role via the adoption of male dress and a beard in the images that she had carved of her. Whether she affected the same items of apparel in life is, again, not knowable.

All this is disputed, though, and it's certainly true that Hatshepsut only caused herself to be represented as male some time after she began to rule. I discuss all this in much more detail in an earlier thread that you can read here:

Did Ramses II try to erase Queen Hatshepsut from the record books because she was a successful ruler or because she was a woman (whom depicted herself as male)?