This study aims to analyze the asymmetry between both eyes of the same patient for the early diagnosis of glaucoma. Two imaging modalities, retinal fundus images and optical coherence tomographies (OCTs), have been considered in order to compare their different capabilities for glaucoma detection. From retinal fundus images, the difference between cup/disc ratio and the width of the optic rim has been extracted. Analogously, the thickness of the retinal nerve fiber layer has been measured in spectral-domain optical coherence tomographies. These measurements have been considered as asymmetry characteristics between eyes in the modeling of decision trees and support vector machines for the classification of healthy and glaucoma patients. The main contribution of this work is indeed the use of different classification models with both imaging modalities to jointly exploit the strengths of each of these modalities for the same diagnostic purpose based on the asymmetry characteristics between the eyes of the patient. The results show that the optimized classification models provide better performance with OCT asymmetry features between both eyes (sensitivity 80.9%, specificity 88.2%, precision 66.7%, accuracy 86.5%) than with those extracted from retinographies, although a linear relationship has been found between certain asymmetry features extracted from both imaging modalities. Therefore, the resulting performance of the models based on asymmetry features proves their ability to differentiate healthy from glaucoma patients using those metrics. Models trained from fundus characteristics are a useful option as a glaucoma screening method in the healthy population, although with lower performance than those trained from the thickness of the peripapillary retinal nerve fiber layer. In both imaging modalities, the asymmetry of morphological characteristics can be used as a glaucoma indicator, as detailed in this work.