I usually buy both versions of a game so as to build different teams. I also don't mind playing as either character.
For example in Y I played as Calem and in X I play as Serena.
The weird thing is that sometimes I get it into my head that the male character should have certain pokemon and the girl should have others. For example, if ever I play as Leaf, Lyra or Serena, they can have Nidoqueen, but not Nidoking, whereas Red, Ethan and Calem can have Nidoking but not Nidoqueen.
Since FireRed/LeafGreen came out, whichever game I get first I keep the saved game on it forever. Ten years later, LeafGreen still contains the saved game that was on it first with most of the pokemon above level 80 (grinding only) and also contains examples of nearly every pokemon available in generation 3, boxed in correct Pokedex order (one Bulbasaur, one Ivysaur, one Venusaur, one Charmander etc.)
One thing that I've tried to do before but never followed through on it until X&Y is to develop many teams. To me these teams represent each player character, rival and main series game. For example I have Charizard, Jolteon, Nidoking, Gengar, Lapras and Snorlax on one team which I unofficially call "Red's Team" then there's Venusaur, Ninetales, Clefable, Nidoqueen, Vaporeon and Dragonite as "Leaf's Team", Blastoise, Arcanine, Alakazam, Rhyperior, Machamp and Fearow as "Blue's Team" and Raichu, Starmie, Pidgeot, Tauros, Vileplume and Flareon as "Yellow's Team"
And so on for Gold, Silver, Crystal, Ruby, Sapphire, Emerald, Diamond, Pearl, Platinum, Black, White, Grey (instead of Black2/White2), X, Y and "Z"