In both cases that you mentioned(i.e. polar coordinates and cube sphere mesh), if you keep the number of cells constant, then the farther you go your cell need to cover more surface, hence, less dense, or lower resolution. So, both would suffer from the same problem.
If you want the cells to have a constant area (regardless of how far you are from the center), then you need to increase the number of cells, which in polar means reducing your dRho and dPhi.
Note that the number of cells increase with second power of R (or distance from the center). So if you are twice away from the center, then you need at least 4 times more cells to have the same density of cells.
You could get some other methods, but then you need to provide more info on how the data is generated or calculates. Generally some more details. But the above general approach would work, but not necessarily the optimum for certain cases.
