In this paper, we investigate the performance of conventional cooperative sensing (CCS) and superior selective reporting (SSR)-based cooperative sensing in an energy harvesting-enabled heterogeneous cognitive radio network (HCRN). In particular, we derive expressions for the achievable throughput of both schemes and formulate nonlinear integer programming problems, in order to find the throughput-optimal set of spectrum sensors scheduled to sense a particular channel, given primary user (PU) interference and energy harvesting constraints. Furthermore, we present novel solutions for the underlying optimization problems based on the cross-entropy (CE) method, and compare the performance with exhaustive search and greedy algorithms. Finally, we discuss the tradeoff between the average achievable throughput of the SSR and CCS schemes, and highlight the regime where the SSR scheme outperforms the CCS scheme. Notably, we show that there is an inherent tradeoff between the channel available time and the detection accuracy. Our numerical results show that, as the number of spectrum sensors increases, the channel available time gains a higher priority in an HCRN, as opposed to detection accuracy.