In-band full-duplex systems promise to further increase the throughput of wireless systems, by simultaneously transmitting and receiving on the same frequency band. However, concurrent transmission generates a strong self-interference signal at the receiver, which requires the use of cancellation techniques. A wide range of techniques for analog and digital self-interference cancellation have already been presented in the literature. However, their evaluation focuses on cases where the underlying physical parameters of the full-duplex system do not vary significantly. In this paper, we focus on adaptive digital cancellation, motivated by the fact that physical systems change over time. We examine some of the different cancellation methods in terms of their performance and implementation complexity, considering the cost of both cancellation and training. We then present a comparative analysis of all these methods to determine which perform better under different system performance requirements. We demonstrate that with a neural network approach, the reduction in arithmetic complexity for the same cancellation performance relative to a state-of-the-art polynomial model is several orders of magnitude.