Considering the most widely spread configuration of actuators for low orbit satellites, namely a set of reaction wheels and a set of magnetorquers, we revisit the classical " cross product control law " solution for achieving attitude stabilization and momentum dumping. We show how the classical solution has a quasi-cascade structure that, under a suitable input-to-state (ISS) assumption, can be stabilized by high gain, thereby making the actuators more inclined to saturate. Motivated by this, we propose a revisited version of this control law that transforms the quasi-cascade into a real cascade. Then we show that both strategies are such that the attitude control is affected by the momentum dumping, and that they both require a suitable ISS property. To overcome these drawbacks, we propose a new allocation-based controller which makes the attitude dynamics completely independent of the momentum dumping and induces global asymptotic stability without any ISS requirement. Several formal statements and simulation results support our discussions and highlight the pros and cons of the different control strategies.