In this work, a combination of experimental and quantum mechanical investigations is performed for the study of dichroic absorption properties of melt-processed linear low-density polyethylene (LLDPE) oriented films containing <= 0.5 wt % of either 4,4'-bis(2-benzoxazolyl)stilbene (BBS) or 2,5-bis(5-tert-butyl-2benzoxazolyl)thiophene (BTBBT). The data acquired reveal that the film optical anisotropy and the performances as linear polarizer are strongly dependent on the molecular structure of the chromophore. In particular, the rodlike structure of BBS favors the alignment of the dye along the drawing direction of the PE film, providing dichroic ratios as high as 100 and optical performances as linear polarizer close to the pseudo-affine deformation scheme. On the contrary BTBBT, although characterized by huge anisotropic potentialities, confers the oriented film very poor dichroism and is unsuitable for linear polarizer applications. This behavior is attributed to the more complex banana-shaped structure of BTBBT dye caused by the thiophene 2,5-functionalization that limits the molecule parallel orientation to the drawing direction.