As I know, these 3 EM tools are mainly used for EM simulation and designs. Based on your experiences which EM simulation you find best for your design?
another discussion about this is on https://www.researchgate.net/post/What_is_the_difference_between_a_time_domain_solver_and_a_frequency_domain_solver_in_cst_mws/1
Typically Method of Moments (MoM) is well-suited for radiation and scattering problems, antennas with conductor only geometries, and also for electrically large scatterers and radiators, where there are several fast algorithms which compresses the Green's function interactions to deal with those problems. This is because MoM only discretizes (meshes) the source, and not the solution domain and hence doesn't need a big radiation box in the solution domain to satisfy the Sommerfield Radiation condition at far field. Therefore it solves the problem in less number of mesh elements. Limitations: The matrix of the system is dense and hence provides computational challenge, unless fast algorithms are used.
FEM on the other hand is extremely well suited for dealing with dielectrics, especially when there is inhomogeneity. This is because FEM has volume based tetrahedral meshes, unlike traditional MoM which uses triangular surface-based meshes, and hence can capture the rapid volumetric dielectric variations in its mesh elements. Although, MoM has well defined surface and volume-based dielectric formulations in place, yet FEM wins over owing to sparse matrix in its formulation. Limitations- not suited for electrically large geometries as the number of unknowns (mesh elements) will be high as both source and solution domain including the radiation box is discretized.
The two methods MoM and FEM are frequency-based methods, and hence are more suited when number of frequency points are less, or in other words narrow-band applications. For wideband and UWB antennas and systems, FDTD is an ideal choice as the problem translates to fewer time samples in time domain and hence FDTD is a better option.
As mentioned, Finite Difference Time Domain, which is with finite difference method. For finite element, the extension of FDTD is FETD (Finite element time domain). If your domain is regular, finite difference will be fine. If your domain is irregular, then Finite Element Time Domain would be better.