Dataset contains results of two phase field simulations of coarsening where the Cahn-Hilliard mobility differs by a factor of 100 between the two phases. Interfacial energy is isotropic, and the nominal volume fractions of the phases are 50%-50%. The two simulations represent different initial conditions for coarsening. The simulation "Random noise initial condition" was initialized from random noise and simulated with dissimilar mobilities for its entire duration. In the simulation "Phase-separated initial condition", phase separation and early coarsening (within the first 2e5 iterations) were simulated with constant mobility, and subsequent coarsening was simulated with dissimilar mobilities. These two conditions resulted in different in initial morphologies and transient evolution. The types of data included are raw simulation output, interfacial shape distributions (ISDs), and a spreadsheet of characteristic quantities for the structure. Details regarding the simulation and characterization methods can be found in our paper located at https://doi.org/10.1016/j.commatsci.2019.109418. The authors acknowledge support from the US Department of Energy under Grant No. DE-SC0015394.