Performance of Compton positron emission tomography (PET) is studied in this paper using qualitative and quantitative methods. Lutetium-yttrium oxyorthosilicate (LYSO), lutetium-gadolinium oxyorthosilicate (LGSO), and CdZnTe (CZT) materials are used for Compton PET. LYSO is widely used for conventional PET, and LGSO is a prospective scintillator material for PET detectors. CZT is one of the semiconductor materials that have high energy and position resolution. For conventional PET, only the photoelectric effect is considered a valid interaction for image reconstruction. However, Compton scattering tracing technology is applied for our Compton PET to additionally use Compton scattering events for image reconstruction. It is relatively difficult to use multiple layers for PET made of scintillators, as electronic circuits must be attached to each layer. For this reason, conventional PET generally uses only one layer for each detector module and limits the spatial resolution in the depth direction. In contrast, it is possible for a CZT detector to measure a depth of interest based on the cathode-to-anode signal ratio or electron drift time with relatively simple electronic circuits. Furthermore, CZT materials have high spatial and energy resolutions. Therefore, the position and energy information of the radiation interactions in the detector module can be precisely calculated to determine the interaction sequence, and hence, the information from the Compton scattering can be used for image reconstruction in PET. For this reason, the reconstructed image of CZT PET can show better quality than those of scintillator PETs. The detection efficiency and quality of the reconstructed image are significantly increased by including the Compton scattering effect as a valid interaction process for image reconstruction because Compton scattering has twice the interaction probability of the photoelectric effect at 511 keV. In this paper, the effectiveness of including Compton scattering events for PET reconstruction was evaluated for scintillators and CZT semiconductor detectors. The maximum likelihood expectation and maximization reconstruction method was applied for conventional and Compton PET reconstruction, and the qualities of the reconstructed images were evaluated.