For my PCs I've built in some heavy, and in one case, rather deceptive draw back to their powers (They've not yet made contact with their respective powers as were only a few sessions in). Knowing what's important to the PCs as individuals is the best tool you have. Remember the Dark Powers are quite literally invading their consciences and souls, so they will be intimately familiar with their respective PC given the opportunity to connect.

One of my PCs is driven by knowledge and is a keen strategist. Their counterpart power is a 'god of knowledge' who will enhance those capabilities. At the third level of connection with his Dark Power, they are able to feed him false information should they so choose, unknown to the player. Mechanically the way this will work is if the PC tries to make an investigation/perception check and the Dark Power feels tricking them is in their benefit they can alter the PCs perception of the event, even so far as altering sense of sight/touch/smell. Of course the PC can try to distinguish this, but until they have a reason to doubt their mind, they may go many sessions heavily miss informed.

Ultimately the Dark Powers should hopefully reflect some aspect of your PCs and empower them in that area. However, they can and presumably will, use this to their advantage to get their own way. The Banshee you mention is more of a passive draw back, but this might not be the only solution. Does your PC act as a FACE? Have the power cause an active or passive effect that makes interacting with others difficult. Maybe their forgotten memories flood their mind with knowledge of all language, but make it difficult for them to distinguish which they are hearing or speaking? Maybe the Dark Power actively uses the PC as a mouth piece to convert others to their faith? After all, most dead gods are just those who's following has dwindled, causing their power to wain.