Cutscenes and CGs transition completely smoothly (CGs have been cropped, but aside that, they look particularly good), which is remarkable. It's just instantaneous and really help the story flow without hiccups. Perhaps this is not such a big deal for some, but for someone who used to to experience extremely long load times for these on the PS2 era, this improvement is eye-opening.
Other than that, every little detail from the PS2 version has transitioned beautifully to the small screen with the upgraded visuals. There are exceptions of course, especially when it comes to some of the game's temples and almost all NPCs, which sometimes look like they didn't work on them at all. Also some of the faces might get some time getting used to, specially Tidus with his new, enormous eyes and Rikku's.
And of course, needless to say, the game's colors just pop and are a joy to behold on the OLED screen. The game's amazingly varied color palette was made for this screen.
To get a general idea of how the game looks and runs, take a look at this YouTube video (has already been posted a few times).
http://www.youtube.com/watch?v=4Rrhcog0ZHk
It does a fairly good job at showing how smooth the game runs. HOWEVER, the video is not too sharp. Even playing it on your Vita in HD via the YouTube app doesn't do the game justice on how sharp it looks.
To get a better idea of this, play the video on your Vita as mentioned above (in HD). I'd say that video scores about 6.5 or 7 out of 10 on representing how sharp and detailed the game really looks on Vita.