In this study, a comprehensive comparison about the hardware costs of the original and the modified Izhikevich neuron models and their applications have been presented to the literature. The chaotic behavior, the coupled version, the synchronization applications, and the control of the synchronization states of the original and the modified Izhikevich neurons have been handled and all of these structures have been also emulated with the FPGA-based realizations for the first time. The aim of this article is to show the suitability and the practicality of the Izhikevich neuron model to the electronic realization applications. According to this aim, firstly, the chaotic behaviors of the original and the modified Izhikevich neuron models have been observed with the numerical simulations. Then, the dynamical behaviors of two coupled original and two coupled modified Izhikevich neurons have been examined via the numerical analyses. After that, the synchronization status of two coupled original and two coupled modified Izhikevich neurons have been controlled by the Lyapunov method and these processes have been simulated numerically. Finally, all of these structures have been implemented with the FPGA device, separately. Therefore, it has been overcome the shortcomings in terms of the electronic realization applications of the Izhikevich neuron model. Besides, the device utilizations of the original and the modified Izhikevich neurons in the FPGA-based implementations have been compared inclusively.