There are a lot of technical factors that could honestly play out differently depending on your gender.
Let's make a note that from right now, everything I say is not of or in any shape or form is an attempt to be sexist.
Mentally things can play out differently with how your character handles situations (and this needs to be taken into account if you're going that in depth with your game). For example, a study shows that females can change their moods more frequently than males. So if the after effects of a character's death is a factor, you would have to assume the males would take a mental breakdown much more slowly. Think of a relationship that just went through a break up. You would see, based on the time frame, that possibly males handle the break up more effectively at first. They would be alright and later the next day or so start to take a tole on them. With females it's more possible that they will take the break up instantly and later recover the next day or so. This does not mean that it can't happen the other way around and everyone is different but this is simply a matter of perspective through known studies.
Physically things can play out based on the gender. Again, studies show that males just play out to be much stronger than females (possibly due to long term nature vs. nurture reasons with males being raised to do all the physical work and be bulky while females try to be fragile, nice and so forth due to society's way of looking at things) you would "assume" that the male would be able to fight off much better or move objects better.
Background of the game can be effected by the genders. An easy example would be the above mentioned game that features females ruling one side and males ruling the other in a segregation.
Again, this is all technical things based on how in depth you really want to get into. Let me know if this way any way helpful.
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