Considering the remarkable progress of the Galileo constellation in recent years, the main objective of this study is to evaluate the performance of dual- and single-frequency Galileo-based precise point positioning (PPP), and its contribution to GPS and Galileo integration with different precise products generated by four analysis centers (ACs) within the context of the Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS). For this purpose, the daily observation dataset collected at ten IGS stations over one month was processed in both static and kinematic modes for Galileo-only, GPS-only, and GPS/Galileo PPP scenarios. For dual-frequency PPP, the results demonstrate that while the Galileo-only solutions are highly comparable with GPS-only PPP for the static mode, the mean 3D positioning errors for Galileo-only processes are approximately 1-cm higher than those obtained from GPS-only solutions for all agencies. The analysis to evaluate the influence of Galileo satellites with highly eccentric orbits, namely E14 and E18, on dual-frequency Galileo-only PPP performance indicates that including or excluding these satellites has no significant effect on the results. For single-frequency PPP, which is dependent on the GRAPHIC combination, Galileo-only PPP performs significantly better, approximately 40%, than GPS-only solutions in the static mode, whereas kinematic Galileo-only and GPS-only PPP solutions are quite similar for all agencies except for WHU. In addition, the RMS of observation residuals for Galileo in single-frequency PPP was noticeably lower than that for GPS, demonstrating that the observation quality of Galileo code measurements is better than those of GPS. Among the ACs, Galileo-based PPP solutions applying CODE products produced slightly better results than those obtained for GFZ and CNES/CLS in general, whereas processes using WHU products resulted in a worse performance, both in terms of positioning accuracy and of convergence time. The integration of Galileo with GPS was shown to enhance PPP performance significantly in both static and kinematic modes.