Purpose: (1) To develop a deep learning algorithm to automatically segment structures of the optic nerve head (ONH) and macula in 3D wide-field optical coherence tomography (OCT) scans; (2) To assess whether 3D macula or ONH structures (or the combination of both) provide the best diagnostic power for glaucoma. Methods: A cross-sectional comparative study was performed which included wide-field swept-source OCT scans from 319 glaucoma subjects and 298 non-glaucoma subjects. All scans were compensated to improve deep-tissue visibility. We developed a deep learning algorithm to automatically label all major ONH tissue structures by using 270 manually annotated B-scans for training. The performance of our algorithm was assessed using the Dice coefficient (DC). A glaucoma classification algorithm (3D CNN) was then designed using a combination of 500 OCT volumes and their corresponding automatically segmented masks. This algorithm was trained and tested on 3 datasets: OCT scans cropped to contain the macular tissues only, those to contain the ONH tissues only, and the full wide-field OCT scans. The classification performance for each dataset was reported using the AUC. Results: Our segmentation algorithm was able to segment ONH and macular tissues with a DC of 0.94 $\pm$ 0.003. The classification algorithm was best able to diagnose glaucoma using wide-field 3D-OCT volumes with an AUC of 0.99 $\pm$ 0.01, followed by ONH volumes with an AUC of 0.93 $\pm$ 0.06, and finally macular volumes with an AUC of 0.91 $\pm$ 0.11. Conclusions: this study showed that using wide-field OCT as compared to the typical OCT images containing just the ONH or macular may allow for a significantly improved glaucoma diagnosis. This may encourage the mainstream adoption of 3D wide-field OCT scans. For clinical AI studies that use traditional machines, we would recommend the use of ONH scans as opposed to macula scans.