Thermophilic and mesophilic enzymes differ in the optimal working temperature, due to a structural adaptation: thermophilic enzymes have more stiff surface-exposed loops than their mesophilic orthologs. Human is mesophile, which means that mesophilic enzymes, no matter whether human or bacterial, will work in human more efficiently.
Bjelic, Brandsdal, and Aqvist (2008) Cold adaptation of enzyme reaction rates. Biochemistry 47: 10049-10057; emphasis mine:
[P]sychrophilic, mesophilic, and hyperthermophilic citrate synthases ... have increasingly stronger electrostatic stabilization of the transition state, while the energetic penalty in terms of internal protein interactions follows the reverse order with the cold-adapted enzyme having the most favorable energy term. The lower activation enthalpy and more negative activation entropy observed for cold-adapted enzymes are found to be associated with a decreased protein stiffness. The origin of this effect is, however, not localized to the active site but to other regions of the protein structure.
Aqvist (2017) Cold adaptation of triosephosphate isomerase. Biochemistry 56: 4169-4176; emphasis mine:
The results show that the enzyme from the psychrophilic bacterium Vibrio marinus indeed displays the characteristic shift in enthalpy-entropy balance, compared to that of the yeast ortholog. The origin of this effect is found to be located in a few surface-exposed protein loops that show differential mobilities in the two enzymes. Key mutations render these loops more mobile in the cold-adapted triosephosphate isomerase, which explains both the reduced activation enthalpy contribution from the protein surface and the lower thermostability.