The only way of improving accuracy (or decreasing the difference of result for equivalent atoms) under the framework of on-grid algorithm is using a smaller grid spacing. The result difference of the two atoms cannot be fully eliminated (unless you employ a special grid distribution, which is fully in line with molecular symmetry)

i use the wave function of hydrogen molecule

my algorithm  correctly assigns most of the points to the basin of the hydrogen 1 and hydrogen 2 (the bcp is at (0,0,0), and my nuclear attractors in (0,0,+-0.584)) but in the plane xy where is the bond critical point (points like (0,2,0) (2,2,0) (1.8,2,0)) these kind of points are assigned to the basis of hydrogen 1 so when i want to integrating the density, the density in the basin of hydrogen 1 has major density than basis of hydrogen 2 because if use 41 points of size  in the end of my  algorithm hydrogen1 has 36141 points in the basin and hydrogen2  34460

so i don't know wath to do for improving my algorithm