Cognitive Radio (CR) is an emerging technology that solves the spectrum inefficient problem in licensed spectrum pools by using dynamic spectral access (DSA). Spectrum Handoff plays an important role in DSA to ensure seamless and robust cognitive user (CU) services to maintain CR network (CRN) quality. In this article, we present the analytical model of pool-based spectral handoff process of two different licensing spectral pools under the Heterogeneous spectral environment (HetSE) of both Ad-HOC (opportunistic) and centralized (negotiated) CRNs. The concept of Intra-Pool and Inter-Pool spectrum handoff are considered to investigate the performance of CU in every possible dimension for developing an optimized and effective CRN. The Spectrum Handoff (SHO) performance metrics: probability mass function (PMF), link maintenance probability (LMP) and link failure probability (LFP) of the CU are derived using intra-pool and inter-pool spectrum handoff concepts under HetSE to investigate the characteristics of CRN for both opportunistic and negotiated spectrum access strategies. The results show that both the strategies produce significantly different performance for pool based spectrum handoff under HetSE of CRN. The Monte-Carlo simulation results are also performed Python platform and compare with the theoretical results to validate the proposed model considering both PUs and CUs activity model.