X has Xerneas (left), Y has Yveltal (right)
As a matter of personal taste, Xerneas' stag-like appearance is more in line with classical Pokemon, while Yveltal has more of the over-designed look associated with later generations. Both potentially have interesting applications in a legendary tier with an inordinate number of Psychic and Dragon-types, but being a Flying-type may hurt Yveltal more than help it, since it takes 25 percent damage from Stealth Rock upon switching in while being vulnerable to Kyogre's Ice Beam attack. Like most legendaries though, both Pokemon are more than capable of doing serious damage against high level trainers in the storyline.
It's in the version-exclusive Pokemon that Y rises over X. Pokemon X is home to Clauncher, which evolves into a rather generic mono Water-type. Much more interesting is Skrelp, exclusive to Pokemon Y, which has the potential to become a much more unique Dragon/Poison-type. When you consider that Fairy-types are vulnerable to Poison, it becomes even more interesting. With that in mind, Skrelp and its evolution certainly have the advantage. And with the other two exclusives being Fairy-types that seem to be mirrors of one another, Skrelp is the difference maker.
X has Clauncher (left), Y has Skrelp (right)
Of course, with the Internet being what it is today, it's quite easy to trade for version exclusive Pokemon like Skrelp, which makes the differences almost academic. If you're interested in training up a Skrelp for competitive battle, having immediate access to it in the wild is a little more convenient; but we're a long way from the days of Ruby and Sapphire, when finding another person with a copy of the game was much more difficult. In fact, you could argue that Ruby and Sapphire were the last games in which version exclusive content really, truly mattered.
Ruby and Sapphire not only featured version exclusive Pokemon and legendaries, but unique story elements as well. In Ruby, the villainous Team Magma wants to drain the oceans and leave the earth landlocked; in Sapphire, the equally villainous Team Aqua is keen on doing the exact opposite. Being fire and water-themed, each team has their own unique Pokemon, resulting in some very different boss battles. Emerald would ultimately merge the two storylines and become the "definitive" version, but at the time, it was a neat twist on the usual Pokemon story conventions.
Since then, Pokemon games have had exclusive monsters and even exclusive gym leaders, but nothing really as far-reaching as Ruby and Sapphire. With that, Pokemon X and Y mostly boils down to whether your prefer a story featuring Xerneas or Yveltal. Mostly.
Pokemon X and Y do have one last trick up their sleeves. Each version has an exclusive Mega Evolution for Charizard and Mewtwo--two staples of the original Red and Blue. In Pokemon X, Charizard becomes a Dragon/Fire Pokemon with the ability Tough Claws, which raises its attack whenever it makes physical contact with a foe. Mega Mewtwo X, meanwhile, gains a unique Psychic/Fighting typing. The Pokemon Y variants, for their part, retain their original typing, but gain unique abilities and stat increases of their own. Particularly interesting is Mega Charizard Y, which has Drought--an incredibly valuable ability that strengthens fire attacks, weakens water attacks, and gives many Grass-types all sorts of interesting bonuses. Up until this point, only Groudon and Ninetails have had this ability, which means that weather teams have an interesting new weapon at their disposal.
Mega Charizard X (left), Mega Charizard Y (right)
Mega Mewtwo X (left), Mega Mewtwo Y (right)
But once again, the difference is mostly academic, since Mega Evolution Stones can be traded between versions. In other words, it's pretty easy to get Mega Charizard X into Pokemon Y, and vice versa. Once again, it's mostly a matter of convenience. If for some reason I were lacking an internet connection though, I personally would go for the Mega Charizard X. Not only is it a cooler design, resembling the awesome shiny black version of the original Charizard, but it has a unique typing. Mega Charizard Y may turn out to be better for competitive battling, but for sheer novelty, Mega Charizard X gets my vote.
In any case, when it comes to picking between Pokemon X and Y, it's really okay to judge a book by its cover. Chances are good that you looked at the version exclusives and immediately preferred one over the other. If that's the case, then get that version. Unfortunately (or fortunately depending on your point of view), we're at the point where it doesn't matter that much anymore. Back in the days of Gold and Silver, it really made a difference. Now? Not as much.
Could it matter in the future? Perhaps if Game Freak took the Oracle of Seasons/Oracle of Ages approach and went all out in crafting separate stories for each. Version exclusive dungeons with their own special legendary Pokemon might also do the trick. Otherwise, it sort of feels like Game Freak is making multiple versions out of obligation, or because it artificially inflates sales. Regardless, while there may be a novel twist to be found in the multiple version concept of Pokemon, that twist is pretty much absent in the latest generation, making it perfectly alright to choose based on whether you think "Pokemon X" is a cooler name than "Pokemon Y."
Me? I'm Pokemon X all the way.