I see no challenge here. It's FFIV, hands down.
The FF series is the greatest series of games to ever grace the presence of gaming systems. It doesn't matter if you enjoy first person shooters, sport games, or RPG's... if you started playing FF games, you wouldn't put them down. Their storylines and gameplay can be understood and played by people of any age, any race, and any preference of gaming.
Now, onto FFII/FFIV.
First of all, just by its advancement from its predecessor alone, this should be voted to advance. The first FF was an interesting, addictive, yet tedious and slow RPG with an extensive storyline and a battle system that was a total mimic of Dragon Warrior. At the time, it was completely overshadowed by DW and almost lost in the shuffle. So, designers of Final Fantasy's sequel wanted to make sure that they would correct their previous mistakes and design a game with quicker load times, a better story, better graphics, more exciting gameplay, and a battle system that would have an edge over its competition, Dragon Warrior.
Once FFII was released, it did everything it was set out to do. The game was a complete 180 from it's predecessor, and it far surpassed Dragon Warrior AND it's sequel. The gameplay was dramatically sped up, the graphics were far advanced, the storyline was more in-depth, more characters were introduced for you to use throughout the game, there were more weapons, spells, and the introduction of the greatest thing to ever have been created for RPG games... the Summon spell.
At the time, there were all sorts of games out there that were a dime a dozen in regards to its spellcasting. A lightning bolt here, a flicker of flames there, and a mini-snowstorm was pretty much the standard for most of the magic-using gaming at the time. FFII took those boring graphics and gameplay and brought it to a whole new level. Spells were shown in detail as they stuck their opponents. And as the basic spells advanced in the forms of FIRE2, ICE2, and LIT2, graphically, you could see and FEEL the increase in power. Then, after the third-level spells, you figured you were finished with the spells, just like in Dragon Warrior and FFI. But, creators came up with an idea for spells that would bring enemies to their knees in the form of a being being summoned to cast a spell that caused utter destruction and was both devestating and expensive to use. The basic fire, ice, and lightning spells were overshadowed as you were able to summon the powers of the GODS of lightning, fire, and ice in the forms of Shiva, Ifrit, and Ramuh, as well as other beings such as Titan, Mist, and the King himself, Bahamut.
This game completely overshadowed all other video games at the time and is still fun to play today. I urge everyone to vote for this game, as well as all other games in the Final Fantasy series. Why? Because they all deserve to be the best.