Breakdown time.

Characters:
FFIX
Almost all the characters in Final Fantasy IX had a great deal of character development, even many of the NPCs an temporary characters. This is due, of course, to the most awesome plot mechanic in the history of Final Fantasy. Yes, I speak of Active Time Events.

Most importantly, Kuja, unlike most villains before him, actually had emotions and was acting on reasons other than a desire to rule or destroy the world just for the sake of it.

FFX
In Final Fantasy X, most of the characters hardly had any development at all. I wouldn't go as far as saying that the majority of characters were stock characters, but I felt that most of them were fairly two dimensional. They had some good potential, but making the entire game from the main character's perspective inhibited opportunities to develop characters other than Yuna and Tidus.

FFX's villain (I'm going to go ahead and consider Seymour the main antagonist, as he's the only one that got any development at all) was relatively two dimensional. He was the typical lunatic bent on cleansing the world by wiping it out.

Gameplay
FFIX
Final Fantasy IX had a return to the class system, something that made me very, very happy. Forming an effective party added a level of strategy that some previous Final Fantasy titles lacked (specifically FFVII and FFVIII). I liked the way characters learned skills and latent abilities through the equipment they wore. Others might find such a system tedious (as it undoubtedly is before the AP increasing latent ability becomes available), I rather enjoyed it. The synthesis system was pretty sweet, too, but it's a little frustrating that some equipment is unavailable past certain points in the game, and some of the best equipment available through synthesizing on disc four require such unavailable items.

World map and exploration was pretty much same old, same old, but that didn't really bother me a whole lot.

FFX
Final Fantasy X started off with a fantastic battle system. However, as the game progresses, characters begin to bleed over and lose their individuality. There's no constrictions on the characters. If the characters each had their own individual sphere grids only allowing slight crossovers of skills, I'd like it a bit more. I hated the sphere grid to begin with, though. Weapon customization was pretty sweet, and I enjoyed the new summoning system. The new take on turn-base combat was awesome.

Also, moving away from the world map was a good idea, but I think switching it in FFX was a little premature. The lack of expansive areas to explore made Spira seem awfully small in comparison to other worlds. Had they done something similar to FFXII's territories (of which I'm not sure they were yet capable) Spira could have been a lot more engaging world.

Music
FFIX
I regard FFIX's soundtrack as a whole to be Nobuo's greatest work. Although many of the songs (such as the over-world theme) are just the tune of the theme song (Melodies of Life), the OST boasted an exceptional number of great songs.

FFX
I'll admit that FFX has a good soundtrack, but very few songs stick out at me (although I love both Auron's and Jecht's themes). It was certainly more diverse than FFIX's OST, but it had less songs that stood out at me.

Plot
FFIX
The plot of FFIX just rocks. Although it does sometimes delve a little too deeply into some more philosophical concepts without really addressing them in a meaningful manner, all the characters drove the plot. I wouldn't consider the plot particularly complex, but it was hardly blunt.

FFX
FFXs plot, unfortunately, was. Aside from two plot twists (Tidus's realization that Yuna will die upon the completion of her pilgrimage and learning that he was merely a product of the dreams of the Fayth), the game was pretty straightforward: travel around collecting summons until you're powerful enough to take down the big baddie.

I won't bother comparing graphics. Pitting a PSX game against a PS2 game just isn't fair as there's a significant leap in the capabilities of each machine.

Final Fantasy X was an enjoyable game, but it's not one I've ever been able to finish a second time (the only Final Fantasy game I've completed that I've not been able to play through a second time, actually). I despise FFVIII more than just about any other game I've ever played, mostly due to the plot, but the gameplay is good enough (and the Triple Triad is bad-ass enough) that I've played through it three times.

As far as I'm concerned, Final Fantasy IX wins by a mile. There really is no contest. Remember what Kishi said, "Only horrible idiots dislike FFIX," (he said it, not me).