This work proposes an analytical framework to study how relay selection strategies perform in half- and full-duplex deployments by combining renewal theory and stochastic geometry. Specifically, we assume that the network nodes -- operating in either half- or full-duplex mode -- are scattered according to a two-dimensional homogeneous Poisson point process to compute the relay selection cost by using a semi-Markov process. Our results show: ($i$) fixed relay outperforms the reactive option in either cases, ($ii$) the performance of both reactive and fixed relay strategies depends on the self-interference attenuation in full-duplex scenarios, evincing when they outperform the half-duplex option, and ($iii$) the reactive relay selection suffers from selecting relays at hop basis, while the fixed relay selection benefits most from the full-duplex communication.