This research reports a comparison of the Unstructured Conservative Level Set (UCLS) method and the Coupled Volume of Fluid-Level Set (VoF-LS) method for the Direct Numerical Simulation (DNS) of hydrodynamics and mass transfer in bubbles using 3D unstructured meshes. The UCLS method presents excellent mass conservation of fluid phases and accurate computation of surface tension force, as well as efficient implementation on unstructured meshes and parallel computing platforms. On the other hand, the coupled VoF-LS method incorporates excellent mass conservation of fluid phases using the geometric Volume-of-Fluid method and accurate computation of surface tension force by using signed distance functions, reconstructed geometrically from the minimum distances to the interface. Concerning the numerical approach, the finite-volume method discretizes transport equations on 3D collocated unstructured meshes. Unstructured flux-limiter schemes discretize the convective term of transport equations. The diffusive term of the transport equations is discretized by the central difference scheme, while the pressure-velocity coupling is solved by the fractional-step projection method. Validations against empirical correlations from the literature are performed for both methods. Finally, the advantages and disadvantages of UCLS and VoF-LS methods on unstructured meshes are analyzed.