During the character creator at the start you can pick between the genders, is there any reason to pick one over the other? Does a male character have any traits or perks a woman has or vice versa?
The short answer is no, there is no difference between male or female. One is not stronger or more intelligent than the other. However, there is actually an advantage to choosing one over the other.
So most importantly, the character will be the same no matter what. Stats are completely unaffected by gender. It would open a world of pain for the developer if it did. The advantage lies in the perks. In this case, it works in favor of choosing a female character. There are two perks that are gender specific. Ladykiller and black widow. The perks give the user advantages when dealing with members of the opposite sex. For example, new dialog options if you are a woman speaking to man and the same the other way around. Along with extra dialogue options, you also gain the ability to do more damage to the opposite sex.
The vast majority of the enemies in the Fallout games are male. If you choose to be male, you won’t get any advantages when dealing with them. If you pick a female, you will now have a perk that gives you extra damage against most of the enemies in the game. Since there is absolutely no other difference between genders, it makes sense to pick female. If you play in first person you will never really see the difference anyway.