Well, 'customization system' would be better than battle system.

Overview time!

FFI: You choose jobs at the beginning, which get upgraded later.

FFII: A realistic customization system. 'Create a character', as they say. Certainly more complex than FFI's system.

FFIII: The first customizable job system, with different abilities.

FFIV: Traditional leveling. Characters have a set class and gain abilities as they level up, like traditional RPGs.

FFV: FFIII on crack. The amount of customization is greater than ever before. Mix-and-match abilities, and the introduction of the Mime class.

FFVI: I hope you don't miss uniqueness in characters, because it's gone. Espers can teach magic, possibly a precursor to the GF Junction system in FFVIII. While characters have certain job-specific abilities and equipment restrictions, everyone can learn every spell.

FFVII: Materia system gives even greater customization. All characters have a suggested job by their starting materia, but in the end, everyone is just separated by their limit breaks.

FFVIII: Junction system is similar to FFVI's system, but now even more abilities are added. Stocking magic to increase your stats gives characters even more power; but is rather unbalanced.

FFIX: Characters learn abilities from different equipment. Nice and smooth.

FFX: The Sphere Grid allows even more flexibility, but each character is somewhat restricted by class. (Unless you fight the superbosses, at any rate.)

X-2: Dresspheres are a nice version of the classic job system. Different Garment Grids offer different abilies and styles. And, you can change jobs in battle. Pretty awesome.

*yawn* That's all I'll do for now.

Anyway, I enjoy Job systems like III, V, and X-2 the best.