Both the global neuronal workspace (GNW) and integrated information theory (IIT) posit that highly complex and interconnected networks engender perceptual awareness. GNW specifies that activity recruiting frontoparietal networks will elicit a subjective experience, whereas IIT is more concerned with the functional architecture of networks than with activity within it. Here, we argue that according to IIT mathematics, circuits converging on integrative versus convergent yet non-integrative neurons should support a greater degree of consciousness. We test this hypothesis by analyzing a dataset of neuronal responses collected simultaneously from primary somatosensory cortex (S1) and ventral premotor cortex (vPM) in nonhuman primates presented with auditory, tactile, and audio-tactile stimuli as they are progressively anesthetized with propofol. We first describe the multisensory (audio-tactile) characteristics of S1 and vPM neurons (mean and dispersion tendencies, as well as noise-correlations), and functionally label these neurons as convergent or integrative according to their spiking responses. Then, we characterize how these different pools of neurons behave as a function of consciousness. At odds with the IIT mathematics, results suggest that convergent neurons more readily exhibit properties of consciousness (neural complexity and noise correlation) and are more impacted during the loss of consciousness than integrative neurons. Last, we provide support for the GNW by showing that neural ignition (i.e., same trial coactivation of S1 and vPM) was more frequent in conscious than unconscious states. Overall, we contrast GNW and IIT within the same single-unit activity dataset, and support the GNW.A number of prominent theories of consciousness exist, and a number of these share strong commonalities, such as the central role they ascribe to integration. Despite the important and far reaching consequences developing a better understanding of consciousness promises to bring, for instance in diagnosing disorders of consciousness (e.g., coma, vegetative-state, locked-in syndrome), these theories are seldom tested via invasive techniques (with high signal-to-noise ratios), and never directly confronted within a single dataset. Here, we first derive concrete and testable predictions from the global neuronal workspace and integrated information theory of consciousness. Then, we put these to the test by functionally labeling specific neurons as either convergent or integrative nodes, and examining the response of these neurons during anesthetic-induced loss of consciousness.