We present a comparative study between two members of serine and aspartic proteases complexed with a peptide substrate. The same computational setup is used to characterize the structural, electrostatic, and electronic properties for the Michaelis complex of furin, a serine protease, and of the aspartic protease from HIV-1. In both cases plane-wave density functional theory (PW-DFT) and empirical force-field-based molecular dynamics calculations are used. For furin, calculations are extended to the complex with the intermediate of the first step of the reaction. Comparisons are also made with results from recent PW-DFT investigations on both families of enzymes and with the same chemical groups in an aqueous environment. It is found that the substrate carbonyl group is more polarized in the furin complex than in the HIV-1 protease one. A further difference regards the large-scale motions of the complexes as a whole and local conformational fluctuations at the active site. The global and local fluctuations are well coupled for HIV-1 protease but not for furin. Thus, despite some chemical analogies in the first step of the reaction mechanism, furin and HIV-1 protease complexes appear to be characterized by a different interplay of electrostatics and conformational fluctuations.