We consider an energy harvesting transmitter sending messages to two users over a vector broadcast channel. Energy required for communication arrives (is harvested) at the transmitter and a finite-capacity battery stores it before being consumed for transmission. Under off-line knowledge of energy arrivals, we obtain the trade-off between the performances of the users by characterizing the maximum departure region in a given interval. We show that the optimal total transmit power policy that achieves the boundary of the maximum departure region is the same as the optimal policy for the scalar single-user channel, which does not depend on the priorities of the users. The optimal total transmit power is found by a directional water-filling algorithm and the optimal splitting of the power among the users and the parallel channels is performed in each epoch separately.