The proper design and configuration of the swing drive mechanism of a hydraulic excavator are crucial to improve energy consumption and efficiency and ensure operational stability. This paper analyzes the influence of the relationship between the parameters of a hydraulic motor and a reducer, which form the integrated transmission of a swing drive, the dynamic characteristics of a hydraulic excavator on loading, and the dynamic stability of the drive. The analysis deals with an excavator model that has the same parameters of the kinematic chain members, the same parameters of the upper structure drive mechanisms, and two variants of the swing drive that, with different integrated transmission parameters, provide the upper structure with the identical number of revolutions and equal rotating moment. One swing drive variant possesses an integrated transmission with a hydraulic motor with a low specific flow and a reducer with a high transmission ratio, while the other drive variant has the opposite parameters. Understanding this relationship is essential for optimizing the design of excavators to achieve better performance and dynamic stability under varying operational conditions. As an example, this paper provides the analysis results regarding the influence of the relationship between the parameters of the integrated transmission hydraulic motor and reducer on the loading and dynamic stability of the swing drive in a tracked hydraulic excavator of 100,000 kg in mass and 4.4 m3 in loading bucket volume, as obtained from the developed dynamic mathematical models of the excavator using the MSC ADAMS program. The results indicate that the dynamic loads on the swing drive’s axial bearing are higher in the variant with a low-specific-flow motor and high transmission ratio reducer during the acceleration and deceleration phases. However, this configuration demonstrated better dynamic stability, with lower oscillation amplitudes and shorter damping times compared to the variant with a high-flow motor and low transmission ratio. Those findings provide valuable criteria for the optimal synthesis of swing drive mechanisms in large hydraulic excavators using multi-criteria optimization methods.