Green shipping and efficient information sharing deepen the collaboration between shipping companies and ports, enabling vessel speed optimization (VSO) to be integrated with the berth allocation and quay crane assignment problem (BACAP). However, the literature presented to date usually considers all vessels as a whole and only addresses the vertical conflict between the two levels of the BACAP and the VSO but neglects the horizontal conflict among vessels in each level of the collaborative planning. To describe and address the conflicts within and between levels, we consider the vessel service differentiation (VSD) and propose a BACAP-VSO with VSD (BACAP-VSO-w/-VSD) collaboration mode. To this end, we set up a bi-level multiobjective optimization model. In the upper-level BACAP model, the VSD is implemented by separating vessels into different preferential groups. Multi-objectives are formulated to minimize the service delays of vessels in preferential groups and all vessels. In the lower-level VSO model, the VSD is realized by grouping vessels based on their shipping companies. Multi-objectives are solved to minimize the fuel consumption costs of each shipping company. We develop a nested genetic algorithm incorporated with an inheritance factor and jumping operations for the solution approach. Experimental results show that the proposed collaboration mode can analyze trade-offs among multiple conflicting objectives in any and between both planning levels. Compared to the existing collaboration mode, the proposed collaboration mode further reduces service delays of vessels and fuel consumption costs of shipping companies, improves customer satisfaction, and effectively reduces vessel emissions.