The Timepix3 is a photon counting semiconductor detector that enables to simultaneously measure the energy and time of arrival of each incident X-ray photon. These properties, along with the high spatial resolution and high efficiency, due to the CdTe sensor material, can be exploited for several imaging applications, such as X-ray phase contrast imaging (XPCI). XPCI relies on the phase shift suffered by X-rays when traversing the sample. This study focuses on the free-space propagation XPCI and single mask edge illumination XPCI methods, which are two approaches that are well suited for laboratory implementations. Since both techniques are highly sensitive to charge-sharing, the Timepix3 energy and time information for each photon are used to minimize this effect by using pixel clustering methods. In addition, the performance of both XPCI techniques across a 30kVp source spectrum is studied using the energy-resolving capabilities of the detector. In both cases, the phase contrast and signal-to-noise ratio (SNR) are assessed as a function of different energy. Finally, it is demonstrated that phase contrast enhancement is feasible with pixel clustering and energy-selection for both XPCI techniques.