This research examines a two-way relay network consisting of two transceivers and multiple parallel relays, which are equipped with single antennas and operate in a halfduplex mode. In this system, the two transceivers prefer to exchange their information via relays. It is assumed that the relays have the full instantaneous channel state information (CSI) and relay the signals using the amplify-and-forward (AF) method. The performance of two AF bi-directional network beamforming schemes, namely multiple access broadcast channel (MABC) strategy and time division broadcast channel (TDBC) protocol, under joint optimal power control and beamforming design are studied and compared. To do so, we first design a TDBC-based bi-directional network beamformers, through minimization of the total power consumed in the whole network subject to quality of service (QoS) constraints, for the case with a direct link between the two transceivers. The corresponding power minimization problem is carried out over the transceiver transmit powers as well as relay beamforming weights, thus resulting in a jointly optimal power allocation and beamforming approach. We devise optimal secondorder cone programming based solutions as well as fast gradient-based solutions to these problems. Then these solutions are exploited to compare the performance of the underlying TDBC-based approach to that of the MABC-based technique developed in [1]. This comparison is important because the TDBC approach appears to have certain advantages which can be exploited towards improving the performance of two-way network beamforming. These advantages include the additional degree of freedom as well as the possibility of benefitting from the availability of a direct link between the two transceivers. Interestingly, in the absence of a direct link between the two transceivers, we show that when the QoS constraints are imposed to meet certain given probabilities of un-coded error (or, equivalently, to meet certain signal-to-noise ratio constraints), these two schemes perform closely in terms of the minimum total transmit power. However, when the QoS iv constraints are used to guarantee certain given rates, the MABC-based scheme outperforms the TDBC counterpart. In the case when a direct link exists between the two transceivers, the TDBC-based approach can outperform the MABC-based method provided that the direct link is strong enough. / UOIT