Owing to the developments of satellite-based and network-based real-time satellite precise products, the Precise Point Positioning (PPP) technique has been applied far and wide, especially since the PPP-B2b service was provided by the third-generation BeiDou Navigation Satellite System (BDS-3). However, satellite outages during dynamic application lead to significant degradation of the accuracy and continuity of PPP. A generally used method is integrating PPP with Inertial Measurement Units (IMUs) to enhance positioning performance. Previous works on this topic are usually based on IMU data at a high sampling rate and are mostly implemented in post-processing mode. This paper will carry out a compressive assessment of the impacts of different types of precise satellite products (real-time products from the CAS, DLR, GFZ, WHU, and the final one from GFZ), Doppler observations, and different sampling rates of IMU data on the performance of the tightly coupled integration of the BDS-3 B1I/B2b and the Inertial Navigation System (INS). Results based on a group of on-board experimental data illustrate that (1) the positioning accuracy with products supplied by the CAS and WHU are roughly consistent with those using the final products; (2) the Doppler observations can effectively improve the accuracies of velocity, attitude, and vertical position at the initial epochs and during the reconvergence periods, but have invisible influences on the overall positioning, velocity, and attitude determination; and (3) the impact of IMU data interval on the performance of PPP/INS tightly coupled integration is insignificant when there are enough available satellites. However, the divergent speed of position is visibly affected by the IMU sampling rate during satellite outage periods.