In this article, we consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs coexist with the uplink (UL) of cellular ground users (GUEs). Our analysis focuses on comparing two spectrum sharing mechanisms: i) overlay, where the available time-frequency resources are split into orthogonal portions for U2U and GUE communications, and ii) underlay, where the same resources may be accessed by both link types, resulting in mutual interference. We evaluate the coverage probability and rate of all links and their interplay to identify the best spectrum sharing mechanism. Among other things, our results demonstrate that, in scenarios with a large number of UAV pairs, adopting overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance. We also find that increasing the density of U2U links degrades their rates in the overlay-where UAVs only receive interference from other UAVs-, but not significantly so in the underlay -- where the effect of GUE-generated interference is dominant.