I remembered once reading that, ironically, Balthier and Fran actually fire slower with guns and bows respectively than other characters. Found this mechanics FAQ that clarifies that the following character and weapon combinations act slightly slower than others: Fran with a Bow, Penelo with a Gun or Crossbow, and Baltheir with any of those three weapons. Past these exceptions, all attack action times are the same so each character performs equally in the speed department (assuming matching stats).
Past this, the relevance is the actual weapon stats. I believe this is explained in one of the game help sections but the following weapons rely on the following stats to deal damage (I'm ignoring which defense they target for now):
- Swords, Spears, Crossbows, Rods, Poles - STR only
- Maces - MAG only
- Katanas, Staves - STR and MAG
- Axes, Hammers, Handbombs - STR and VIT
- Daggers, Ninja Swords, Bows - STR and SPD
- Guns, Measures - no stats; these will always do the same damage no matter who uses them, basically, though remember who is slower with guns.
The FAQ linked earlier will go into more detail if you want to read the specifics of how it all works. The differences usually aren't a lot to make a humongous difference barring license/equipment focus towards certain stats. All the same, the top three characters in each stat over time are:
- STR - Basch, Vaan, Balthier
- MAG - Ashe, Penelo, Vaan
- VIT - Vaan, Penelo, Balthier
- SPD - Balthier, Vaan, Fran
For the most part these differences aren't humongous (and by the time they hit the larger gaps, you'll possibly be hitting the damage cap anyway), so it shouldn't impact, but if you wanted to prioritize based on stat, this would be the direction to head.