The deployment of 5G private networks has enabled ultra-reliable low-latency communication and high-throughput capabilities essential for physical bilateral teleoperation and immersive virtual reality (VR) applications. However, the performance of these applications is inherently affected by the underlying network configuration, including factors such as the deployment mode. In this work, we present a comprehensive end-to-end performance profiling of bilateral teleoperation and immersive virtual applications under two 5G private network deployment models: (i) a cloud-native 5G leveraging virtualized RAN and cloud-native core functions and (ii) a fully physical 5G network. The results demonstrate that while the hybrid deployment achieves flexibility and scalability, it incurs increased latency variance and jitter due to virtualization overheads compared to the physical deployment which maintains lower end-to-end delays and jitter, ensuring deterministic performance, particularly in high-precision teleoperation scenarios.