Well they do work at different scales. You use phase field to model the response of a system at the macro or micro scale similarly to continuum mechanics (micron up to cm scale or even m scale).

While MD is more discrete type modeling. Simulating the response individual atoms etc. So you are down to Angstrom or nanoscale.

Usually you calculate material properties with MD and feed them into your macroscopic phase field model.

MD is computationally demanding while phase field is over simplified technique.

It isn't right to compare which one is better; as they are complementary to each other. You could use both of them in order to develop a more microstructure-informed model.

Well they do work at different scales. You use phase field to model the response of a system at the macro or micro scale similarly to continuum mechanics (micron up to cm scale or even m scale).

While MD is more discrete type modeling. Simulating the response individual atoms etc. So you are down to Angstrom or nanoscale.

Usually you calculate material properties with MD and feed them into your macroscopic phase field model.

MD is computationally demanding while phase field is over simplified technique.

It isn't right to compare which one is better; as they are complementary to each other. You could use both of them in order to develop a more microstructure-informed model.

FYI:

Early solidification is investigated using two different simulation techniques: the molecular dynamics (MD) and the phase-field (PF) methods. While the first describes the evolution of a system on the basis of motion equations of particles, the second grounds on the evolution of continuous local order parameter field. The phase-field is a powerful method to describe solidification phenomena on the mesoscopic length scale. It has been used to model homogeneous and heterogeneous nucleation, microstructure formation in solids, and motion of grain boundaries. The phase-field models include formulations for pure substances, for multicomponent systems, and for polycrystalline structure and solidification in eutectic, peritectic, and monotectic systems. Other simulation techniques for dendrite growth are cellular automata and hybrid methods such as the multiscale diffusion Monte Carlo (DMC). The phase-field method requires previous knowledge of the material properties of the system in study. The input includes bulk properties such as density, heat capacity and latent heat, and others such as interfacial and kinetic growth coefficients, being the latter properties which are hardly accessible in experiments. Here molecular simulations play a fundamental role, since they provide a link between an interaction potential and all the required properties. Kinetic coefficients, interfacial free energies, and their dependence on the crystal orientation, of pure metals and alloys, can be directly obtained from simulations of inhomogeneous liquidcrystal systems.

cited from 2013 Phase-field simulations at the atomic scale in comparison to molecular dynamics