In the neuroscience field, the comparative study was used to identify the similarities and differences of the neural network across species. The comparison based on the computational approach was recently used because this technique can identify the structural and functional similarities across species. The critical system is one of the network properties that commonly used as the comparison indicator. Therefore, we used the vulnerability analysis to identify the critical systems based on three fundamental network properties: global efficiency, global betweenness centrality and global clustering coefficient. Our study focused on identifying the similarities and differences between Caenorhabditis elegans (C. elegans), Drosophila melanogaster (fruit fly) and Mus musculus (mouse) because these three species are the most common species in the connectomics studies. Our study identified three important findings. First, the structure of the critical systems in advanced species is more systematic and efficient than the structure of the critical systems in simpler species. Second, the similarity of the primary functions exists in the critical interneuron and motor parts across species. However, the interneuron and motor part of advanced species has high cognitive functions, while this function has not been found in simpler species. Third, the critical sensory in each species depends on their activity time and environmental condition. From these results, we predict the similarity between human and fruit fly in the critical sensory area. We also predict the similarity between human and mouse in critical interneuron and motor parts.