Interconnecting power converters (IPCs) are the main elements enabling the interconnection of multiple high-voltage alternating current (HVac) and high-voltage direct current (HVdc) subgrids. To ensure stable operation of the resulting hybrid ac/dc systems, grid-following (GFL) and grid-forming (GFM) controls need to be carefully assigned to individual IPC terminals when using common IPC controls. In contrast, dual-port GFM control imposes a stable voltage on the ac and dc terminals and can be deployed on all IPCs regardless of the network configuration. In this work, we use hybrid ac/dc admittance models, eigenvalue sensitivities, and case studies to analyze and quantify the underlying properties of ac-GFM control, ac-GFL, and dual-port GFM control. Compared to common ac-GFM and ac-GFL controls, dual-port GFM control: 1) renders IPCs dissipative over a much wider range of frequencies and operating points; 2) significantly reduces the sensitivity of IPC small-signal dynamics to operating point changes; and 3) exhibits an improved dynamic response to severe contingencies. Finally, the results are illustrated and validated in an experimental scaled-down point-to-point HVdc system.