Despite extensive research on sliding mode control (SMC) design for quadrotors, the existing approaches suffer from certain limitations. Euler angle-based SMC formulations suffer from poor performance in high-pitch or -roll maneuvers. Quaternion-based SMC approaches have unwinding issues and complex architecture. Coordinate-free methods are slow and only almost globally stable. This paper presents a new six degrees of freedom SMC flight controller to address the above limitations. We use a cascaded architecture with a position controller in the outer loop and a quaternion-based attitude controller in the inner loop. The position controller generates the desired trajectory for the attitude controller using a coordinate-free approach. The quaternion-based attitude controller uses the natural characteristics of the quaternion hypersphere, featuring a simple structure while providing global stability and avoiding unwinding issues. We compare our controller with three other common control methods conducting challenging maneuvers like flip-over and high-speed trajectory tracking in the presence of model uncertainties and disturbances. Our controller consistently outperforms the benchmark approaches with less control effort and actuator saturation, offering highly effective and efficient flight control.