The aim of this study was to conduct an experimental comparative analysis of the stability of axially compressed thin-walled closed-section profiles with identical geometries, manufactured from PLA, PETG, PETG-CF, and ABS thermoplastic materials using fused deposition modeling (FDM), and from a carbon–epoxy CFRP composite with a quasi-isotropic stacking sequence. The profiles had square cross-sections with internal dimensions of 40 × 40 mm, a height of 200 mm, and a wall thickness of 1.24 mm. Three specimens were manufactured from each FDM material, resulting in a total of 12 profiles. Axial compression tests were conducted using a universal testing machine, an ARAMIS 2D digital image correlation system, and an acoustic emission system. The critical loads were determined from the experimental load–displacement curves using the intersection method based on fitted straight-line segments. Among the thermoplastic materials, the highest mean critical load was obtained for PLA; it was approximately 1.29 times higher than that obtained for PETG, 1.70 times higher than that obtained for PETG-CF, and 1.36 times higher than that obtained for ABS. The mean critical load of the CFRP profile was approximately 13.9 times higher than that of the PLA profiles. Five complete buckling half-waves were observed in the PLA, PETG, and ABS structures, seven in the PETG-CF structures, and four in the CFRP profile. Despite substantial differences in the critical load values, the experimental load–displacement responses and the overall buckling behavior of the investigated structures were similar. The acoustic emission signals recorded near the critical state did not indicate the initiation of permanent material damage, as confirmed by the absence of stiffness degradation and the recovery of the specimens’ original shapes after unloading. The novelty of the present study lies in the comparison of the behavior of thin-walled structures manufactured using FDM additive technology with that of thin-walled composite structures. The obtained results may provide a basis for assessing the applicability of additive manufacturing technologies in the design of thin-walled load-bearing structures.