A clinical trial named PROMETHEUS is currently ongoing for inoperable hepatocellular carcinoma (HCC) at the Heidelberg Ion Beam Therapy Center (HIT, Germany). In this framework, 4D PET-CT datasets are acquired shortly after the therapeutic treatment to compare the irradiation induced PET image with a Monte Carlo PET prediction resulting from the simulation of treatment delivery. The extremely low count statistics of this measured PET image represents a major limitation of this technique, especially in presence of target motion. The purpose of the study is to investigate two different 4D PET motion compensation strategies towards the recovery of the whole count statistics for improved image quality of the 4D PET-CT datasets for PET-based treatment verification. The well-known 4D-MLEM reconstruction algorithm, embedding the motion compensation in the reconstruction process of 4D PET sinograms, was compared to a recently proposed pre-reconstruction motion compensation strategy, which operates in sinogram domain by applying the motion compensation to the 4D PET sinograms. With reference to phantom and patient datasets, advantages and drawbacks of the two 4D PET motion compensation strategies were identified. The 4D-MLEM algorithm was strongly affected by inverse inconsistency of the motion model but demonstrated the capability to mitigate the noise-break-up effects. Conversely, the pre-reconstruction warping showed less sensitivity to inverse inconsistency but also more noise in the reconstructed images. The comparison was performed by relying on quantification of PET activity and ion range difference, typically yielding similar results. The study demonstrated that treatment verification of moving targets could be accomplished by relying on the whole count statistics image quality, as obtained from the application of 4D PET motion compensation strategies. In particular, the pre-reconstruction warping was shown to represent a promising choice when combined with intra-reconstruction smoothing.