Breaker uses axes and hammers and such, and gets the four breaks (Wither, Expose, Addle, Shear) without requiring an esper for thembecause in IZJS there's a LOT of individual licenses blocked off by a blank space that needs to be filled in with an esper - so you have to choose between powerups for different characters sometimes.
The machinist uses guns mainly, and also measures and bombs. The Hunter uses daggers and ninja blades, and I suppose fits the 'thief' job class the best. Although since Vaan, Balthier and Fran all have the Steal license by default, that in itself is not gonna be a problem.