The aspect common in the variation of oxidation state within group 13 (B to Tl) and group 14 (C to Pb) is that of inert pair effect.
As we move down the group (13 or 14), we find that the lower oxidation state becomes more stable. In case of group 13 elements, it is +1 oxidation state that becomes stable while in group 14 it is +2 oxidation state that becomes stable. This behaviour can be understood if we consider the fact that as we move from the 2nd period to the 3rd a d-subshell is added.
Similarly, upon moving further down the group there is an f-subshell which is added. f-subshells have a poor shielding effect. As a result, the s-electrons in the heavier elements of the 13th and 14th group are held more tightly and thus, are reluctant to get oxidised.
This causes the lower oxidation state to become more stable.