Situations where I pick a female character over a male when both are available:
- It noticeably changes gameplay or story
- I'm on playthrough 10+ of an RPG and I'm starting to somewhat RP characters rather than just be 'myself, but game protagonist"
Examples for the former are rare, and the word "noticeable" is pulling a lot of weight:
People were talking about Dishonored 2 above, for me it would probably qualify since Emily gets a different moveset/gameplay to Corvo's.
I've been told FemShep's voice actress in Mass Effect gives a different enough performance (especially if going Renegade) that it's worth doing a female run at least once, even if the story itself doesnt really change.
Elden Ring is one of my few examples of the latter: I've done so many fucking playthroughs that I now RP characters as a way to decide what build I'm sticking to for this run and what order to explore things.
In games where basically everything is the same like The Eternal Castle, I just play as a Male. Skyrim is an obvious one, but I'd consider Oblivion and Morrowind to be similar as I don't think the starting Stat differences are enough (especially in the long run) to make it matter.
EDIT: I also just thought of the Mount & Blade games, but I don't know too much about deeper mechanics in those. As far as I'm aware, playing as a woman amounts to having a big debuff to your relations with NPCs and Lords. If that IS all it is, I really only perceive it as basically a 'challenge run', which in sandboxy games just means a long tedious process to get back to baseline stats and then it's just a normal run from there (read: Kenshi Torsolo runs that are just several days of grinding for artificial limbs, and then it's just a normal run with a long preamble).