The Cout equation in the MAX16833 datasheet and in Application Note 5571 is functionally the same. The difference lies in the definition used for the output voltage ripple Voutripple. The MAX16833 datasheet assumes equal contributions of output voltage ripple for the output capacitor ESR and the output capacitance. Therefore, Voutripple / 2 = ΔVq_out = ΔVesr_out.