It's better by about 1.5 effective DEX in a vacuum. However, because of Accuracy needs, the Ningi actually ends up being slightly better before you have the AS4 body. If you use the Void Ark body, you need to use the Fabled Aiming Neck (high Acc/low SS) instead of the Gordian one (low Acc, high Det)

http://ffxiv.ariyala.com/SH5P [Ningi: 1310.422 effective DEX].

http://ffxiv.ariyala.com/SH5Q [Void Ark: 1308.112 effective DEX].

Is that worth spending 825 Eso and a Gobtwine to get, especially if you already have the Void Ark body? 2 effective DEX is pretty small, so probably not. If you've already got the Ningi though, you're better off using a Farthing from Void Ark to upgrade it to 210 and not spending Esoterics (and a Gobcoat) on the inferior accessory.

Obviously, if you're not doing Savage, Accuracy is of no consequence, so the Void Ark body is better.