I've thought of a couple ways that gender could play a bigger role in the games. I had a third but it was a stretch. Please read and comment. And if you guys don't like the second option I'll just delete it.
Gender affecting strength, speed and potency - Let's say if a male version of a Pokemon (according to Dex) has sharper claws or talons, he could have a higher ATK than a female or a greater chance at a critical hit. Or let's say a female version of a Pokemon has a more potent poison, she could have a greater chance of poisoning another Pokemon than a male does. The same goes for how fast they run, how hard their shell/body is, etc. It'll all depend on what the Pokedex says about them and won't refer to every single Pokemon but certain ones where the males and females differ greatly.
Gender affecting Natures - This may come off as sexist but males could have a greater chance at being Adamant or Hasty while females could have a greater chance at being Calm or Sassy. Nothing will be written in stone. All of the Natures will still be available to each gender but the gender will make boost the chances of a certain Nature being assigned to a Pokemon.
Gender affecting strength, speed and potency - Let's say if a male version of a Pokemon (according to Dex) has sharper claws or talons, he could have a higher ATK than a female or a greater chance at a critical hit. Or let's say a female version of a Pokemon has a more potent poison, she could have a greater chance of poisoning another Pokemon than a male does. The same goes for how fast they run, how hard their shell/body is, etc. It'll all depend on what the Pokedex says about them and won't refer to every single Pokemon but certain ones where the males and females differ greatly.
Gender affecting Natures - This may come off as sexist but males could have a greater chance at being Adamant or Hasty while females could have a greater chance at being Calm or Sassy. Nothing will be written in stone. All of the Natures will still be available to each gender but the gender will make boost the chances of a certain Nature being assigned to a Pokemon.