Hybrid AC/DC microgrid clusters are key building blocks of smart grid to support sustainable and resilient urban power systems. In microgrid clusters, the subgrid load-priorities and power quality requirements for different areas vary significantly. To realize optimal power exchanges among microgrid clusters, this paper proposes a decentralized self-optimizing power control scheme for interlinking converters (ILC) of hybrid microgrid clusters. A priority-driven optimal power exchange model of ILCs is built considering the priorities and capacities in subgrids. The optimization objective is to minimize the total DC-voltage/AC-frequency state deviations of subgrids. To realize the decentralized power flow control, an optimal-oriented quasi-droop control strategy of ILCs is introduced to not only achieve a flexible self-optimizing power flow management, but also provide an ancillary function of voltage support. Consequently, as each of ILCs only monitors the local AC-side frequency and DC-side voltage signals, the whole optimal power control of the wide-area microgrid clusters is achieved in a decentralized manner without any communication link. Thus, the proposed control algorithm has the features of decreased cost, increased scalability, reduced geographic restrictions and high resilience in terms of communication faults. Finally, the proposed method is validated by case studies with four interconnected microgrids through hardware-in-loop tests.