Job levels affect how many times a character attacks during their turn as well as minor damage algorithms. It also raises the success rate of certain abilities like Steal. You'll need a Job Level of 70 or higher in Thief, to successfully steal Gungir from Odin as an example.

The only stat that has a major impact on your characters is Vitality, which affects how much HP you get when you level up. For example, keeping a character in mage related classes will have much lower health than a character who primarily uses melee-centric classes.