Laminated composites based on polyetheretherketone (PEEK) and polyimide (PI) matrices were fabricated by hot compression. Reinforcing materials (unidirectional carbon-fiber (CF) tapes or carbon fabric) and their layout patterns were varied. Stress–strain diagrams after three-point flexural tests were analyzed, and both lateral faces of the fractured specimens and fractured surfaces (obtained by optical and scanning electron microscopy, respectively) were studied. It was shown that the laminated composites possessed the maximum mechanical properties (flexural elastic modulus and strength) in the case of the unidirectional CF (0°/0°) layout. These composites were also not subjected to catastrophic failure during the tests. The PEEK-based composites showed twice the flexural strength of the PI-based ones (0.4 and 0.2 GPa, respectively), while the flexural modulus was four times higher (60 and 15 GPa, correspondently). The reason was associated with different melt flowability of the used polymer matrices and varied inter- (intra)layer adhesion levels. The effect of adhesion was additionally studied by computer simulation using a developed two-dimensional FE-model. It considered initial defects between the binder and CF, as well as subsequent delamination and failure under loads. Based on the developed FE-model, the influence of defects and delamination on the strength properties of the composites was shown at different stress states, and the corresponding quantitative estimates were reported. Moreover, another model was developed to determine the three-point flexural properties of the composites reinforced with CF and carbon fabric, taking into account different fiber layouts. It was shown within this model framework that the flexural strength of the studied composites could be increased by an order of magnitude by enhancing the adhesion level (considered through the contact area between CF and the binder).