I am trying to decide which ability score to put my half-elf +2 bonus into: Charisma or Intelligence. It seems like Charisma is important for a bard, but Intelligence governs the many Knowledge skills a bard is skilled in. Which is more important for an arcane duelist bard, Charisma or Intelligence?
Strength or Dexterity
And Dexterity only if you are using Dervish Dance.
Neither Charisma nor Intelligence are incredibly important for the Combat Bard.
Intelligence governs Skills, but a Bard has a lot of them anyway. Arcane Duelists loses a lot here. Skills are not your primary concern anymore if you take that Archetype. Since you lose Bardic Knowledge, your Bard does not specialize in Knowledge at all.
Charisma mostly governs Spell DCs, and a small number of bonus spells per day. If you stay clear of anything that allows a save and focus on buffing yourself (Heroism, Haste, Feather Step, etc.), that is not your concern. Honestly, you will never reach the DCs needed to effectively use some of the spells, since you are dependent on STR, DEX, CON and CHA.
I play a melee bard in PFS with 19 STR at level 8, INT 10 and CHA 14. He is a good skillmonkey, and just Power Attack Cleave Arcane Strikes with his longsword wielded in two hands, and it works wonderfully. I don't have the (or any) Archetype, and I can't say I miss it. I would miss Versatile Performance, though.