Spectrum handoff (SHO) is an essential technique in dynamic spectrum access policy to guarantee seamless and robust service of a cognitive radio. Link maintenance probability (LMP), link failure probability (LFP), service completion probability (SCP), probability mass function (PMF), and expected number of SHOs are key measuring metrics to characterize SHO performances in cognitive radio vehicular centralized network (CR-VCNET) and cognitive radio vehicular ad-hoc network (CR-VANET). In this paper, we develop and model the performance measuring parameters for a non-stationary cognitive user (CU) considering both complete service and incomplete service period under two CR network situations: opportunistic situation (OS or CR-VANET) and negotiated situation (NS or CR-VCNET). This paper analyzes the impact of CU mobility and spectrum hole mobility on various performance measuring metrics to explore the characteristics and performance of the CR networks. This paper also presents the comparison results for expected number of SHOs and SCP of a CU with and without mobility in both CR-VCNET and CR-VANET. The results of performance metrics obtain for a non-stationary CU under the impact of service time distributions are significantly different for CR-VCNETs and CR-VANETs. In addition, we also present Monte-Carlo simulation of LMP, LFP, and probability mass function of SHO for a non-stationary CU to validate the proposed model.