In this paper, we consider two fundamental full-duplex (FD) architectures, two-node and three-node, in the context of cellular networks where the terminals employ directional antennas. The simultaneous transmission and reception of data in non-orthogonal channels makes FD radio a potential solution for the currently limited spectrum. However, its implementation generates high levels of interference either in the form of loopback interference (LI) from the output to the input antenna of a transceiver or in the form of co-channel interference in large-scale multicell networks due to the large number of active links. Using a stochastic geometry model, we investigate how directional antennas can control and mitigate the co-channel interference. Furthermore, we provide a model which characterizes the way directional antennas manage the LI in order to passively suppress it. Our results show that both architectures can benefit significantly by the employment of directional antennas. Finally, we consider the case where both architectures are employed in the network and derive the optimal values for the density fraction of each architecture which maximize the success probability and the network throughput.