Full-duplex (FD) technology is envisaged as a key component for future mobile broadband networks due to its ability to boost the spectral efficiency. FD systems can transmit and receive simultaneously on the same frequency at the expense of residual self-interference (SI) and additional interference to the network compared with half-duplex (HD) transmission. This paper analyzes the performance of wireless networks with FD multi-antenna base stations (BSs) and HD user equipments (UEs) using stochastic geometry. Our analytical results quantify the success probability and the achievable spectral efficiency and indicate the amount of SI cancellation needed for beneficial FD operation. The advantages of multi-antenna BSs/UEs are shown and the performance gains achieved by balancing desired signal power increase and interference cancellation are derived. The proposed framework aims at shedding light on the system-level gains of FD mode with respect to HD mode in terms of network throughput, and provides design guidelines for the practical implementation of FD technology in large small-cell networks.