Necklace of the Depths: Det. 1, Wis. 1, Pers. +1, HP +20, MP +20
Amulet of Dark Whispers: Stun Immunity, Awa. +2, HP -25, MP +50
In general, the unique item Amulet of Dark Whispers is considered "better" for a mage, esp when fighting monsters that are stun-locking you. But, a lot of it will depend on your playing style, where you are in the game, and if you're struggling to stay alive.
The Amulet of Dark Whispers is the ONLY item in the game that gives Mages Stun Immunity, that by itself is a pretty sizable benefit given how squishy mages become if stunned. The +2 AWA is also useful for passing certain in-game trait checks.
The big draw backs to the Amulet of Dark Whispers is of course the reduced HP. Mages tend not to have a lot of life to spare so given up 25 hit points is pretty noticeable, esp in the early to mid-game.
The Necklace of the Depths isn't a bad item. It gives a nice assortment of benefits. The total difference in HP between the two amulets is 45 (20, -25,) so the HP difference really stands out in a direct comparison. The +1 PERS can also add MP to the mage (see traits for more details).
So if you're not fighting monsters that are stun-locking you, you might find the Necklace of the Depths a better go-to piece of your standard equipment.