Short double-skin concrete-filled steel tube (CFDST) columns can exhibit improved axial performance when externally confined with fiber-reinforced polymer (FRP); however, direct experimental evidence comparing glass- and carbon-fiber-reinforced polymer (GFRP and CFRP) systems under otherwise identical CFDST conditions remains limited. In this study, this research gap was investigated through a controlled experimental program in which the column geometry, steel tube specifications, concrete mix design, curing conditions, fabrication process, and loading protocol were kept consistent across all specimens, while only the FRP system was varied, using either one layer of bidirectional GFRP or one layer of bidirectional CFRP. A total of nine circular, short CFDST columns were tested under axial compression, and their responses were evaluated in terms of ultimate load-carrying capacity, secant stiffness, ductility, post-peak strength degradation, and energy absorption. The results showed that the secant stiffness increased by 11.44% for CFRP and 5.65% for GFRP. The ductility index also increased by approximately 9.87% in the GFRP specimens, whereas a reduction of approximately 14.4% was observed in the CFRP specimens. Energy absorption increased for both FRP systems over the tested displacement range. Since the tensile strength, elastic modulus, ultimate strain, and nominal thickness of the two FRP systems were not mechanically matched, the observed differences should be interpreted as differences in the performance of the specific FRP systems used in this experimental program rather than as evidence of the inherent or general superiority of one fiber type over the other. Accordingly, the findings provide a controlled basis for selecting an FRP system according to the intended design objective—prioritizing stiffness and strength or deformation capacity—within the range of geometry, materials, and loading conditions investigated.