The reactions of piperonylic acid (HPip) and cinnamic acid (HCinn) with 4,4’-bipyridine (4,4’-bipy) have been assayed using the same synthetic methodology, yielding two binary cocrystals with different acid:4,4’-bipy molar ratios, (HPip)(4,4’-bipy) (1) and (HCinn)2(4,4’-bipy) (2). The melting point (m.p.) of these cocrystals have been measured and a remarkable difference (ΔT ≈ 78 °C) between them was observed. Moreover, the two cocrystals have been characterized by powder X-ray diffraction (PXRD), elemental analysis (EA), FTIR-ATR, 1H NMR spectroscopies, and single-crystal X-ray diffraction. The study of their structural packings via Hirshfeld surface analysis and energy frameworks revealed the important contribution of the π···π and C-H···π interactions to the formation of different structural packing motifs, this being the main reason for the difference of m.p. between them. Moreover, it has been observed that 1 and 2 presented the same packing motifs as the crystal structure of their corresponding carboxylic acids, but 1 and 2 showed lower m.p. than those of the carboxylic acids, which could be related to the lower strength of the acid-pyridine heterosynthons respect to the acid-acid homosynthons in the crystal structures.