Autistic children (AT) are known to exhibit distinct postural control patterns compared to neurotypical (NT) children. However, identifying and interpreting these differences can be complex due to the wide range of variables used to analyse Centre of Pressure (CoP) trajectories. This study aims to elucidate the specific characteristics of postural control in AT children by identifying the most discriminative CoP variables that distinguish them from NT children. The study evaluated 24 AT and 24 NT children while they stood on a force plate for 30 s under three conditions: eyes open (EO), eyes closed (EC), and the feet on a foam pad with eyes open (EOF). A total of 75 variables—including frequential, linear, and non-linear variables—were extracted from the CoP trajectory. These variables, expressed as the rate of change between the EC and EOF conditions relative to the EO condition, were compared between the AT and NT groups. A best-subsets approach was used to identify the most discriminative variables, and Pearson correlations were calculated to assess their relationship with age and Social Responsiveness Scale (SRS) scores. Of the 75 variables analysed, 15 showed significant differences between the AT and NT groups. The best-subsets analysis and the correlations revealed that variables such as the rate of change between the EOF and EO conditions, and the root mean square of the trembling component of the CoP trajectory, were particularly discriminative. Autistic children demonstrated a more rigid and regular CoP trajectory, particularly in the EO condition, compared to NT children. These findings suggest that AT children have greater difficulty integrating multisensory information and an increased reliance on supraspinal processes for postural control.