I think my largest improvements in Pokémon playing came in GSC and RSE. I transitioned from Red, where I hardly caught any Pokémon, only used my starter, and didn't pay attention to any stats besides HP, to Gold, where I made a full team and completed my Pokedex. Sure, my Gold team was bad, but at least it was an improvement. I first got into the competitive aspects of Pokémon in Sapphire, when I learned about EVs and IVs and started using balanced, effective teams.
In answer to the poll's question, though, I haven't improved a whole lot in XY. I do think I've become a better/more avid breeder--the new mechanics have encouraged me to do a lot more IV breeding, as I actually feel like I have some control over it now. As for actual battling abilities, I generally just breed/raise competitive Pokémon without actually using them in battles against other real players, so I doubt I've improved that much. Sure, I know a lot of common Pokémon, counters, etc., but I don't have the damage calculations memorized that a lot of high-end players seem to. Will move A from Pokémon B (with EV spread C) OHKO or 2HKO Pokémon D with EV spread E? I probably couldn't tell you, but I could make a reasonable guess as to how other players might respond to certain situations.