Double attack rate up increases Burst damage too, as it allows you to Burst more often. Double attack is particularly nice because you can stack it on frontliners and get the full effect. Of course, if your Soul is your bottleneck for Bursts this won't change that.
So how do accessory buffs stack up?
+ATK (+3% max) has a 0.45% return in damage for each additional 1% at 120% character ATK, or +1.35% damage for a max-level accessory. As a rule of thumb, take the nominal effect and divide by 2 for the true effect on damage.
Double attack (+2%) directly modifies normal attack damage and can modify Burst damage as well if it contributes to more frequent Bursts. As such, it's best used on frontliners. Using a build with Shiva where the damage breakdown for normal/skill/Burst damage was 51/20/29%, +Double attack adds 1-1.6% damage, depending on whether it's contributing to more frequent Bursts or not. That range will also fluctuate somewhat depending on skill damage contribution to overall damage. So on a bottleneck character, double ATK would be better, while on others +ATK might be better. As a rule of thumb, take the nominal effect and divide by 2 for the true effect on normal attack damage.
+Ability damage (+5%) is worse than +ATK unless the ability has a base modifier of < 3.7. If we're going to buff abilities and nothing else we want to see at least a 2x difference, so cut that to < 2. The ability should also do significantly more unbuffed total damage than a normal attack to be worth buffing; 4x would be a reasonable cutoff. Put these together and the ability needs at least 3 hits to benefit significantly from +Ability damage on accessories, with SR characters' weak damage skills disqualified pretty much by default. You could probably say that about +ability damage in general.
+Burst damage (+5%) is useless because, like +ability damage, it adds to a modifier that is already greater than 1. For SR+ kamihime, that's 3.5+, essentially nerfing the effect to the same as +ATK or less. Burst builds can expect even less return since they'll be using temporary buffs to raise that base modifier even higher. This stat exists to trick players who don't understand the damage formulas. As a general rule, take the nominal effect and divide by 5 to get the true effect.
+HP% (+3%) is straightforward. But you should already have +HP from Defender weapons, so the effect will be somewhat reduced. Only recommended for kamihime with low HP or frontliners. Otherwise use Defender weapons and eidolons to manipulate HP for your entire team at once.
+DEF (+3%) decreases damage by a little less than 3%. Use this to enhance survivability of vulnerable frontliners or essential characters, especially with low HP and no DEF bonuses. Use this over +HP% when possible since it benefits more from healing. Otherwise, the same caveats as +HP% apply.
+Affliction rate up (+2%) is the best effect for Single-element builds. You want this on any ATK or DEF debuffer whose abilities ever miss. Debuffs missing is the #1 reason for wipes in content you can usually clear, so less missing = fewer wipes. Since DEF down is directly linked to damage output, 2% less chance of missing > +2% damage, which makes +Affliction rate superior to even +ATK for damage when equipped on your debuffers, and since debuffs typically have a team-wide effect you can multiply that by 5!
Drop rate up is valuable for farming. Assuming you like farming efficiently, having these in your progression gear isn't a waste. Make sure you keep all Rs with this, as they're free to unequip.