We consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs share the same spectrum with the uplink (UL) of cellular ground users (GUEs). For this setup, we focus on analyzing and comparing the performance of two spectrum sharing mechanisms: (i) underlay, where the same time-frequency resources may be accessed by both UAVs and GUEs, resulting in mutual interference, and (ii)overlay, where the available resources are divided into orthogonal portions for U2U and GUE communications. We evaluate the coverage probability and rate of both link types and their interplay to identify the best spectrum sharing strategy. We do so through an analytical framework that embraces realistic height-dependent channel models, antenna patterns, and practical power control mechanisms. For the underlay, we find that although the presence of U2U direct communications may worsen the uplink performance of GUEs, such effect is limited as base stations receive the power-constrained UAV signals through their antenna sidelobes. In spite of this, our results lead us to conclude that in urban scenarios with a large number of UAV pairs, adopting an overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance.