The ductility and axial load-carrying performance of square ultra-high-performance concrete (UHPC)-filled stainless-steel tubular (UHPCFSST) columns compared with that of square UHPC-filled steel tubular (UHPCFST) columns is an intriguing research question worthy of exploration. Twenty-seven square UHPCFSST columns were designed and tested under axial compression. The variables include the outside breadth B (80 mm, 100 mm, and 120 mm) and wall thickness t (4 mm, 6 mm, and 8 mm) of stainless-steel tubes. The axial compression performance and cooperative load-carrying mechanisms of square UHPCFSST columns were quantitatively evaluated, including the failure modes, stress–strain relationships, size effects, and ductility. The stress–strain curves can be divided into three types based on hoop confinement coefficient (ξs). Quantitative analysis was conducted on the sensitivity of the parameters affecting the load-carrying capacity. A clear negative correlation exists between the strength index SI and breadth-to-thickness ratio B/t. As the steel content ratio α increased, the load-carrying capacity enhancement factor λ of stainless-steel tube also increased. A database of square UHPCFST columns containing 187 specimens was constructed. A predictive model for the axial load-carrying capacity of square UHPCFSST and UHPCFST columns was established. Comparative analysis of the models showed the high accuracy and rationality of the proposed model.