If the springs are without any load, then the kinetic energy internal to the spring should be the same.

The case of basketball is different. Energy is lost to inelastic deformation, which is proportional to the area involved. The kinetic energy of the deformed part should be negligible.

If all deformation is elastic, but there is a load on top of the spring. Then the spring's internal energy upon bouncing from the ground is sort of proportional to the mass ratio between the spring and the load, but independent of the spring constant (assuming it is not too small such that the load effectively collides with the ground).