This paper aims to investigate the impacts of sensing energy and data availability on the secondary throughput of energy harvesting cognitive radio networks (EH-CRNs), where secondary transmitters (STs) are powered by the energy harvested from primary radio frequency (RF) signals. To reach the aim, we consider two extreme cases by employing two data arrival processes: heavy data arrival and general data arrival. In the heavy data arrival case, we consider STs always have data to transmit, and study the impacts of sensing energy on the secondary throughput. In the general data arrival case, we consider the data arrives with a certain probability, and study the impacts of data availability (i.e., data arrival probability and data buffer capacity) on the secondary throughput. Moreover, to compare the secondary throughput under non-cooperative spectrum sensing (NCSS) and cooperative spectrum sensing (CSS), we further study two CRN scenarios for each data arrival case: Scenario 1 with one pair of secondary users (SUs) conducting NCSS, and Scenario 2 with multiple pairs of SUs conducting CSS. As the harvest-then-transmit protocol is employed by STs, it is essential to balance energy harvesting and data transmission to achieve high secondary throughput. We thus utilize an energy threshold approach to determine the actions of each ST. Specifically, under the heavy data arrival, we derive the average secondary throughput for each scenario by taking the sensing energy as an energy unit and modeling the energy states of each ST as a Markov chain. Under the general data arrival, we derive the secondary throughput for each scenario by modeling the energy and data states of each ST as a two-dimensional Markov chain. Simulation results show that: (1) both the secondary throughput and the optimal energy threshold decrease with the sensing energy; (2) the secondary throughput increases with the data availability, while the optimal energy threshold decreases with the data availability; (3) from the normalized secondary throughput perspective, CSS is not always better than NCSS.