For commercial EM solvers, I would say FEM is the most popular. Ansys HFSS and Maxwell are FEM, CST is FEM and a bit of MoM from what I've read (Method of Moments). ADS Momenta uses MoM. I know Sim4life, a medical EM software suite, uses FDTD method.
FEM can certainly solve in the time domain as well. I'm not really well enough versed to know when a FEM method becomes less/more efficient than a FDTD method in terms of parallelization and RAM. But if you are ever using a commercial solver, you are probably using FEM. I have taken a Computational EM class and I can tell you I find FDTD much more intuitive. As such its probably more popular for those making custom codes. Fortunately we live in a day where commercial EM solvers are very powerful and flexible, slowly removing the need for custom EM solver.