Ability damage up is pretty much useless for characters without multi-hit skills.

The stat difference in ATK between maxed SR and SSR accessories is about 600, or 1.5% of a character's total. Double ATK up has a 2% chance of adding an attack at max level (essentially a 2% damage increase). As you can see, 1 good skill can make a LV40 SR better than a LV50 SSR, and with a lot less investment.