If I had to rate the stories overall...

Tanks: DRK > GNB > WAR > PLD

Heals: SCH > AST > WHM

Melee DPS: DRG > SAM > NIN > MNK

Ranged DPS: MCH > BRD > DNC

Magic DPS: SMN > BLM > RDM

DRK is a very "personal" story...and I can't say much more about that without it becoming spoilery.

DRG can be considered a prelude to HW in a way and changes the dialogue throughout a fair bit if you opt to finish the level 50 quests prior to starting it.

SCH offers some additional insight into the Nymians, the lesser known third party in the War of the Magi.

MCH ties rather strongly into the social climate of Ishgard and the push towards giving the commonfolk more power and presence in a society where some would rather they stay down in the dirt.

SMN offers a fair bit of additional lore behind the Allagans, has some appearances from MSQ characters, and also has the distinction of being the only job story that has any direct Ascian involvement.

I have reasons why I liked all of the stories in general, but I find those ones had the most reasons I liked them overall.