This study establishes a dual-channel supply chain (DCSC) wherein the e-retailer is endowed with superior demand information, and investigates power structure preferences of the supplier and e-retailer. Game models are investigated based on two information structures (information symmetry and asymmetry) and three power structures, i.e., vertical Nash, e-retailer-led Stackelberg, and supplier-led Stackelberg. We derive the optimal solutions under each model and then conduct a deep comparison analysis. The results reveal that the impacts of information asymmetry on the DCSC vary with the power structure, and the DCSC members’ power structure preferences vary with the information structure. Under information symmetry, it is best for DCSC members to move late and is worst for them to move simultaneously. Under information asymmetry, the supplier has the first-move advantage given specific conditions, in which he has the initiative to screen the e-retailer’s private information. Furthermore, by introducing proper contracts, information asymmetry would not always be harmful for the DCSC; in contrast, DCSC members may obtain more ex-ante profits compared with information symmetry.