Quad Photodiode (QPD) sensors represent an evolution by providing four sub-views, whereas dual-pixel (DP) sensors are limited to two sub-views. In addition to enhancing auto-focus performance, QPD sensors also enable disparity estimation in horizontal and vertical directions. However, the characteristics of QPD sensors, including uneven illumination across sub-views and the narrow baseline, render algorithm design difficult. Furthermore, effectively utilizing the two-directional disparity of QPD sensors remains a challenge. The scarcity of QPD disparity datasets also limits the development of learning-based methods. In this work, we address these challenges by first proposing a DPNet for DP disparity estimation. Specifically, we design an illumination-invariant module to reduce the impact of illumination, followed by a coarse-to-fine module to estimate sub-pixel disparity. Building upon the DPNet, we further propose a QuadNet, which integrates the two-directional disparity via an edge-aware fusion module. To facilitate the evaluation of our approaches, we propose the first QPD disparity dataset QPD2K, comprising 2,100 real-world QPD images and corresponding disparity maps. Experiments demonstrate that our approaches achieve state-of-the-art performance in DP and QPD disparity estimation.