This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of them interacting under a mean field game (MFG) framework. Unlike the conventional major-minor player game, the mean field term herein is endogenously determined by the two leaders simultaneously. These homogeneous followers are not cooperative, whereas the two leaders can either compete or cooperate with each other, which are respectively formulated as a Nash and a Pareto game. The complete solutions of the leader-follower game can be expressed in terms of the solutions of some non-symmetric Riccati equations. Conceivably, the two modes of interactions between leaders each has their own merits and neither is always more favourable to the community, i.e., to the followers. While a comparative statics of the effect of different modes of governance on the society is relatively rare in the literature, we attempt to provide some preliminary quantitative analysis on this topic. In particular, under a broad class of practically relevant models, we provide sufficient conditions to decide whether cooperation or competition between leaders is more favourable to the followers via a comprehensive study. Intutively, the relative merits of the two games depend on whether the interests between the two leaders and the followers align with each other. Numerical examples supporting the findings are also provided.