On their privacy terms:
However, for convenience, your Phoenix application delegates the calculation of payment routes to the ACINQ node. In the current version of the wallet, this node will know the final recipient of the payment, and the amount sent. Work is being done to remove that limitation and have better privacy.
So no privacy.
They had the Eclair app before which allowed manual channel management but sadly they retired it. Hopefully they re-introduce something similar in the future version of Phoenix
Zeus has an embedded node now and you configure channel management. Also, keep an eye out for Blixt -- it's not ready for real funds yet but is a full lnd experience on your phone.
