Turmoil is a 10% accuracy + damage + defence boost and then it drains 10% in each from your opponent. You can also wear a necklace such as the Amulet of Souls for a decent damage boost.
Zealots increases the single stat boosting normal prayers by 10%, so that's 16% accuracy, damage and defence. It does not drain your opponent though, so it's only the better necklace for places where you need the accuracy, don't need soulsplit and the opponent cannot have its stats drained.
An example of a good place to use it at would be Araxxor, since there are very few opportunities to soulsplit, you can't drain araxxor/araxxi's stats and you can miss your attacks.