Glaucoma is a silent killer of eyesight that affects people of all ages. The loss of sight from glaucoma is irreversible and usually gradual in nature, with treatments limited to slowing down its progression. Early detection is important to save vision loss. Colour fundus photographs (CFPs) are often used to diagnose glaucoma. In recent years there has been an increasing interest to develop convolutional neural network (CNN)-based approaches for automated assessment of glaucoma using CFPs. CNN models vary notably in network depth, computational cost, and performance. This paper aims to justify whether low computationally intensive CNNs are capable to detect glaucoma as good as high computationally intensive CNNs. With that aim, this paper evaluates the performance of seven state-of-the-art CNNs with varying computational intensity – MobileNetV2, MobileNetV3, Custom ResNet, InceptionV3, ResNet50, 18-Layer CNN and InceptionResNetV2. The publicly available large-scale attention-based glaucoma (LAG) dataset that has been used for experiments. With its 1, 711 “glaucomatous” and 3,143 “non-glaucomatous” sample images, LAG database is the largest publicly available glaucoma dataset to date. Experiments reveal that despite being significantly less computationally demanding, MobileNetV3 outperforms all others, and produces an accuracy, specificity and sensitivity of 97.7%, 97.8% and 97.6%, respectively.