Things I like:
The wide variety of Pokemon - seriously, there were SO many options in this game. It makes it unlikely that you have the same team as other players. It also really adds to the replay value. If I wanted to play it again, I already know I want a Ralts, because I couldn't choose it in my game because I had Fennekin as a Psychic-type already.
Pokemon-Amie - The amount of effort that went into this was astounding. They had to make 3D models for over 700 Pokemon, clearly outline places you could pet, as well as all those minigames which are actually FUN to play. Not to mention, Pokemon-Amie actually has benefits in the main game as well, so you WANT to play it. It's more than just a time-waster. Plus, it makes ANY Pokemon look adorable when you're petting it.
The quick start - I'm surprised how little hand-holding there is in the beginning of the game. They don't even TELL you the Running Shoes are on. In the first rival battle, they don't stop to tell you how the game works like in FRLG. I would have thought it would be dumbed down like other Nintendo games, but there really isn't.
Mega-Evolutions - When I saw these, I thought it was a gimmick, but it's actually a really cool idea. Not only are there a LOT more Mega-Evolutions than I thought there would be, but you get to use one in the game, even if you didn't choose the 'popular' Pokemon that happened to get them. Not to mention, besides Mega Charizard X, none of them look overly stupid because of their 'badass' factor.
Length - This game is a lot longer than usual. Maybe it's because of all the time I wasted catching Pokemon and playing Pokemon-Amie, but I beat the Champion just under 50 hours. I WAS going slowly, but I know I took BW slowly and it didn't take me that long to beat the game.
The new Pokemon - I normally don't care for how Pokemon look, but even I admit a lot of Gen 5 Pokemon were ugly. In Gen 6, they DEFINITELY chose quality over quantity. There were only a few new Pokemon, but they were ALL cool and almost all of them were usable (besides, like, Bunnelby). While I didn't use ALL Gen 6 Pokemon, 4/6 from my team were from Gen 6. And I loved all of them.
Disappointments:
The Story/Characters - I think the problem with the story was there were too many characters, and thus no one got enough focus. After all, we have 4 rivals, not 1 or 2, and they try to develop them at least a little bit. Isn't it weird you only fight Shauna twice, once at the beginning of the game, and once at the end? Heck, we only battle Trevor once! But that made sense story-wise, so it's not a big deal.
As for Team Flare and AZ, they really get the short end of the stick when it comes to screentime. We get NO time for these characters (Lysandre and AZ) to develop. We barely even KNOW who they are before all the reveals start happening. AZ is obviously an attempt at another tragic figure like N, but we only meet him ONCE in passing before the climax. Think about how many times we see and talk to N and even Ghetsis before the end of BW. Most of the Champions get more screentime in the game than AZ does in XY. And speaking of Champions, Diantha gets next to no screentime. Even less than Iris in BW2, I think.
Other wasted characters? The gym leaders. Remember how in Gen 5, the gym leaders actually DID stuff in the plot, making you feel like they were actually authorities and important people? That didn't happen in this game at all. I barely even remember the gym leaders, and many of them like Olympia and Ramon, felt very bland and simply there because they needed 8 gym leaders. Not to mention their personalities ranged from non-existent to cliche.
Difficulty - Unfortunately, XY took one thing I hated about Gen 5, which was giving the gym leaders a max of 3 Pokemon, and the Elite Four only get 4 Pokemon. Why? The gym leaders in this game where a complete joke. And I wasn't even overlevelled. And that's the main problem. With the new EXP share mechanics, it's SO easy to be overlevelled to the point that the entire game is a joke. I kept it off 95% of the time, because I saw how easy it made the game.
Music - OK, a lot of the music in XY is really good like Lumiose City, or the Champion music, or the Legendary music. But the two music pieces I was most interested in, the Gym Leader theme and the Team Flare theme, were really disappointing. They seemed to take a more atmospheric approach to these themes, with less memorable melodies and more accompaniment. Also, they got rid of the 'last Pokemon' remix of the main Pokemon theme in the Gym Leader battles, which really confused me.