The SSR accessories have much higher stat caps. The 500 or so attack gain from an SSR is much more important than 6% (3%*2) higher character attack for one character. Also, you can keep farming until you get approximately the effects you want.I'm not familiar with the games calculation/damage formulas. Would an SR accessory with good effects, like say maybe atk up, be better than a SSR accessory with bad/negligible effect like resist up?
Ancient accessories aren't mentioned in earlier versions of the wiki. They were likely added with rank 5 accessory quests.