In X, my team was Delphox, Gallade, Vespiquen, Aurorus, Golurk, and Blastoise. I also used Heliolisk and Lucario on my team during my playthrough.
My team in Y was Chesnaught, Talonflame, Florges, Goodra, Meowstic (Male), and Lapras. Gengar was also a member of my team for a while.
I picked Fennekin as my starter in X and Delphox turned out to be very useful against the Kalos Gym Leaders and Elite 4. Its Psychic type comes in handy against Korrina and it blazed through Wulfric's team with ease. I originally used Heliolisk on my team, though I swapped it for Vespiquen just to give me a challenge. This game is actually quite hard if you use less powerful Pokémon on your team. I actually struggled against Lysandre since I didn't use a lot of tough 'mons on my team. In addition, I lost the first game against the Elite Four since I didn't use an electric type to easily defeat Siebold's water types. However, my Aurorus with Thunder managed to defeat Siebold's Gyarados. I first used Blastoise with Rain Dance so that Thunder lands 100% against his Pokémon. It's also useful that my Aurorus had Freeze-Dry which is super effective against water types. I picked Squirtle from Professor Sycamore since I really liked Mega Blastoise. It's nice that it can learn Dark Pulse which it gains a boost from the Mega Launcher ability. I used Golurk since I didn't use one in Gen 5, and it was helpful that it can learn powerful moves like Phantom Force.
In Y, I picked Chespin and Chesnaught helped me tremendously against the Elite Four. It's a nice defensive tank and I liked that Chesnaught has a good movepool. Talonflame was useful against Wulfric and fairy types since it can learn Steel Wing. I picked Charmander from Professor Sycamore, though I didn't really use it much since I already had Talonflame as a fire type on my team. My Florges was a handy cleric since it can learn Wish to heal my Pokémon, and Goodra was just a super cuddly dragon that I wanted to use as a team member. I used Gengar with its Mega Evolution to defeat Valerie, though I swapped it with Meowstic because it's one of my favorite Kalos Pokémon. It did somewhat help my team with Light Screen, and it was quite useful against Drasna's Dragalge. I used the Lapras from the guy who gave it as a gift Pokémon, and it managed to defeat Siebold's water types with Rain Dance + Thunder. When I faced Diantha, I used my Talonflame with Steel Wing against Mega Gardevoir and won.
Besides that, I used Vibrava/Gabite against the Clemont's electric types in Lumiose City. You know, I really loved how large the Kalos Dex is, and the region has a variety of Pokémon available early in-game. This gave me a variety of Pokémon to choose from.