Providing seamless connectivity to unmanned aerial vehicle user equipments (UAV-UEs) is very challenging due to the encountered line-of-sight interference and reduced gains of down-tilted base station (BS) antennas. For instance, as the altitude of UAV-UEs increases, their cell association and handover procedure become driven by the side-lobes of the BS antennas. In this paper, the performance of cellular-connected UAV-UEs is studied under 3D practical antenna configurations. Two scenarios are studied: scenarios with static, hovering UAV- UEs and scenarios with mobile UAV-UEs. For both scenarios, the UAV-UE coverage probability is characterized as a function of the system parameters. The effects of the number of antenna elements on the UAV-UE coverage probability and handover rate of mobile UAV-UEs are then investigated. Results reveal that the UAV-UE coverage probability under a practical antenna pattern is worse than that under a simple antenna model. Moreover, vertically-mobile UAV-UEs are susceptible to altitude handover due to consecutive crossings of the nulls and peaks of the antenna side-lobes.