Answer
Neither of the two methods of approximation accounts for the gradual increase in $Z_{eff}$ as we move down a group.
Work Step by Step
Both approaches produce 2 equal estimates of $Z_{eff}$ of Na and K ($1+$ and $2.2+$), so it only concerns with the number of electrons and the nuclear charge.
The gradual increase in $Z_{eff}$ as we move down a group is caused by the more spread the electrons are, or the positions of the electrons. None of the two approaches account for that.
