We investigate the properties of large-scale multi-objective quadratic assignment problems (mQAP) and how they impact the performance of multi-objective evolutionary algorithms. The landscape of a diversified dataset of bi-, multi-, and many-objective mQAP instances is characterized by means of previously-identified features. These features measure complementary facets of problem difficulty based on a sample of solutions collected along random and adaptive walks over the landscape. The strengths and weaknesses of a dominance-based, an indicator-based, and a decomposition-based search algorithm are then highlighted by relating their expected approximation quality in view of landscape features. We also discriminate between algorithms by revealing the most suitable one for subsets of instances. At last, we investigate the performance of a feature-based automated algorithm selection approach. By relying on low- cost features, we show that our recommendation system performs best in more than of the considered mQAP instances.