6-9 was basically the peak and beginning of the decline. All of them (well, with the exception of 9) introduced hugely new mechanics, or really pushed the boundaries of what games could contain - graphical updates, combat systems, 3d world exploration, all the stuff that makes final fantasy a truly great series.
Then they kind of... lost their way. Nobuo leaving in the middle of X really hurt, as his music played more than a small part of the greatness of the earlier games. But X is also where the changes started getting really evident - the company was focused more on a grand spectacle of cutscene chains than any kind of immersive adventure the player gets to experience. FFX, however, was still not totally lost - it ended up being fairly good, definitely not on the level of its 4 predecessors, but still a thoroughly playable JRPG.
And then shit got *really* bad. Square Enix decided that the one thing they hated in their games was players being able to do fucking *anything*. Issuing commands to all your characters in battle? Fuck that, we'll just put in an AI system so you can set up auto-cast spells and if:then statements so you don't actually have to press any buttons in combat. Characters with depth and complexity? Fuck that, we'll make you play as Vaan, a 12-year-old with no connection to the story or any of its other characters, basically watching an epic adventure that *other people are having* from the sidelines with no control, understanding or meaningful involvement. And 13 kept up the awful spiral - very pretty, polished graphics, hours and hours of cutscenes, with the depth of a teaspoon and the actual player involvement of your typical movie (aka none at all).
Anyway, of the actually good Final Fantasy games, it's hard to pick an absolute best. They all had strengths and weaknesses. FF6 introduced a huge cast of characters, and even gave 2 or 3 of them really great plot and backstory, but because so many existed (and some get found really late in the game) most had only very minor story elements or none at all. 6 and 7 both offered a legendary antagonist, each very dangerous and chaotic, but not in a stupid way - the story flawlessly built up to the final confrontation, and there was a lot of emotion invested in the fight. This was probably 8's greatest failure - with the actual "bad guy" being introduced about an hour before the end of the game, it didn't have much of a connection to the rest of the story, and thus felt disjointed and out of place (see also: mass effect 3's ending). But 8 offered a ton of shit to make up for it - character depth and development even in non-playable characters and bad guys like Seifer, who you can't help but root for even though you know he's the bad guy. The biggest open world to explore and a fucking dragon spaceship to do it in. Fantastic cutscene animation (for the time) without cutscenes being "the point" of the game.
Good poll, and it's interesting to see the results - 6 and 9 are pulling ahead of 7 and 8, but all 4 are definitely the best of the Final Fantasy series.