Mobile and IoT operating systems-and their ensuing software updates-are usually distributed as binary files. Given that these binary files are commonly closed source, users or businesses who want to assess the security of the software need to rely on reverse engineering. Further, verifying the correct application of the latest software patches in a given binary is an open problem. The regular application of software patches is a central pillar for improving mobile and IoT device security. This requires developers, integrators, and vendors to propagate patches to all affected devices in a timely and coordinated fashion. In practice, vendors follow different and sometimes improper security update agendas for both mobile and IoT products. Moreover, previous studies revealed the existence of a hidden patch gap: several vendors falsely reported that they patched vulnerabilities. Therefore, techniques to verify whether vulnerabilities have been patched or not in a given binary are essential. Deep learning approaches have shown to be promising for static binary analyses with respect to inferring binary similarity as well as vulnerability detection. However, these approaches fail to capture the dynamic behavior of these systems, and, as a result, they may inundate the analysis with false positives when performing vulnerability discovery in the wild. In particular, they cannot capture the fine-grained characteristics necessary to distinguish whether a vulnerability has been patched or not. In this paper, we present PATCHECKO, a vulnerability and patch presence detection framework for executable binaries. PATCHECKO relies on a hybrid, cross-platform binary code similarity analysis that combines deep learning-based static binary analysis with dynamic binary analysis. PATCHECKO does not require access to the source code of the target binary nor that of vulnerable functions. We evaluate PATCHECKO on the most recent Google Pixel 2 smartphone and the Android Things IoT firmware images, within which 25 known CVE vulnerabilities have been previously reported and patched. Our deep learning model shows a vulnerability detection accuracy of over 93%. We further prune the candidates found by the deep learning stage-which includes false positives-via dynamic binary analysis. Consequently, PATCHECKO successfully identifies the correct matches among the candidate functions in the top 3 ranked outcomes 100% of the time. Furthermore, PATCHECKO's differential engine distinguishes between functions that are still vulnerable and those that are patched with an accuracy of 96%.