The end of FFX just feels immense and final, to me. Sin collapsing down through the clouds before exploding into a blaze of pyreflies, the Aeons fading away and leaving their statues vacant - those scenes captured the sensation of one thousand years of suffering evaporating at last. It's beautiful, but also profound and sad. The musical score really brings it to life - the orchestral Hymn of the Fayth, with a solo oboe as the Aeons are finally laid to rest by Yuna's dancing. Then there's Tidus' departure. He went into that final fight against his own father, knowing that both of them would die if he succeeded. He may be a whiny teenager, but his was a damn brave and selfless sacrifice. Thanks to Tidus' influence, Yuna doesn't have to sacrifice herself to bring peace - but in the end, she has to lose him, and the Aeons, to achieve the ultimate end of Sin.
It's a nice contrast - the worldwide immensity of Sin's death, coupled with the intensely personal conclusion to the story between Yuna and Tidus.
Quality stuff, all in all. FFVII's still my favourite ending out of any of the FF games - I get a kind of cold shiver every time I replay that conclusion - but FFX's a strong contender for second place, let down only by the fact that it's a fairly short and predictable ending.