Today, the security of many domains rely on the use of Machine Learning to detect threats, identify vulnerabilities, and safeguard systems from attacks. Recently, transformer architectures have improved the state-of-the-art performance on a wide range of tasks such as malware detection and network intrusion detection. But, before abandoning current approaches to transformers, it is crucial to understand their properties and implications on cybersecurity applications. In this paper, we evaluate the robustness of transformers to adversarial samples for system defenders (i.e., resiliency to adversarial perturbations generated on different types of architectures) and their adversarial strength for system attackers (i.e., transferability of adversarial samples generated by transformers to other target models). To that effect, we first fine-tune a set of pre-trained transformer, Convolutional Neural Network (CNN), and hybrid (an ensemble of transformer and CNN) models to solve different downstream image-based tasks. Then, we use an attack algorithm to craft 19,367 adversarial examples on each model for each task. The transferability of these adversarial examples is measured by evaluating each set on other models to determine which models offer more adversarial strength, and consequently, more robustness against these attacks. We find that the adversarial examples crafted on transformers offer the highest transferability rate (i.e., 25.7% higher than the average) onto other models. Similarly, adversarial examples crafted on other models have the lowest rate of transferability (i.e., 56.7% lower than the average) onto transformers. Our work emphasizes the importance of studying transformer architectures for attacking and defending models in security domains, and suggests using them as the primary architecture in transfer attack settings.