Note that the total kinetic energy term is simply a multiple of the six-dimensional Laplacian operator. It treats all Cartesian position coordinates exactly the same, regardless of which direction or which electron it is. Is this still the case if other particles are involved?
The kinetic energy of the two electrons is
All else being the same, heavier particles would have less kinetic energy. But, of course, all else is usually not the same. For example, the atoms in noble gases have the same kinetic energy at the same temperature regardless of atom mass.