Utilizing the triboelectric effect of the fibrous structure, a very low cost and straightforward sensor or an energy harvester can be obtained. A device of this kind can be flexible and, moreover, it can exhibit a better output performance than a device based on the piezoelectric effect. This study is concerned with comparing the properties of triboelectric devices prepared from polyvinylidene fluoride (PVDF) fibers, polyamide 6 (PA) fibers, and fibrous structures consisting of a combination of these two materials. Four types of fibrous structures were prepared, and then their potential for use in triboelectric devices was tested. Namely, individual fibrous mats of (i) PVDF and (ii) PA fibers, and their combination—(iii) PVDF and PA fibers intertwined together. Finally, the fourth kind was (iv), a stratified three-layer structure, where the middle layer from PVDF and PA intertwined fibers was covered by PVDF fibrous layer on one side and by PA fibrous layer on the opposite side. Dielectric properties were examined and the triboelectric response was investigated in a simple triboelectric nanogenerator (TENG) of individual or combined (i–iv) fibrous structures. The highest triboelectric output voltage was observed for the stratified three-layer structure (the structure of iv type) consisting of PVDF and PA individual and intertwined fibrous layers. This TENG generated 3.5 V at peak of amplitude at 6 Hz of excitation frequency and was most sensitive at the excitation signal. The second highest triboelectric response was observed for the individual PVDF fibrous mat, generating 2.8 V at peak at the same excitation frequency. The uniqueness of this work lies in the dielectric and triboelectric evaluation of the fibrous structures, where the materials PA and PVDF were electrospun simultaneously with two needles and thus created a fibrous composite. The structures showed a more effective triboelectric response compared to the fibrous structure electrospun by one needle.