Automated methods for Alzheimer's disease (AD) classification have the potential for great clinical benefits and may provide insight for combating the disease. Machine learning, and more specifically deep neural networks, have been shown to have great efficacy in this domain. These algorithms often use neurological imaging data such as MRI and FDG PET, but a comprehensive and balanced comparison of the MRI and amyloid PET modalities has not been performed. In order to accurately determine the relative strength of each imaging variant, this work performs a comparison study in the context of Alzheimer's dementia classification using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset with identical neural network architectures. Furthermore, this work analyzes the benefits of using both modalities in a fusion setting and discusses how these data types may be leveraged in future AD studies using deep learning.