Satellite orientation is a fundamental component of processing high-precision data from the Global Navigation Satellite System (GNSS). However, insufficient handling of satellite orientation may substantially affect the quality of the precise point positioning (PPP) solutions. This research investigates the influence of satellite orientation using satellite attitude quaternions on the third-generation BeiDou Navigation Satellite System (BDS-3) PPP. To illustrate the impact of satellite attitude, both float and PPP with integer ambiguity resolution (PPP-AR) were undertaken using observations from a multi-GNSS Experiment (MGEX) network. To fully evaluate the effect of the quaternions on PPP, a comprehensive comparison between BDS-3 and Galileo constellations was conducted using nominal attitude and quaternions. The findings indicate a significant performance difference between BDS-3 and Galileo satellites in phase observations after resolving integer ambiguities, with Galileo consistently demonstrating superior phase residuals across various receivers. When it comes to positioning accuracy, the utilisation of quaternions improves coordinate precision across both constellations. Furthermore, the quaternions enhance the stability of time series for the positioning biases and observational residuals.