In Group 13 elements, the stability of the higher oxidation state (+3) decreases down the group, while the stability of the lower oxidation state (+1) progressively increases due to the inert pair effect (the reluctance of the valence $ns^2$ electrons to participate in bonding). For the heaviest element, Thallium (Tl), the +1 oxidation state is much more stable than the +3 oxidation state. Therefore, $TlI$ is significantly more stable than $TlI_3$. Conversely, for lighter elements like Al, the +3 state is most stable, meaning $AlCl_3 > AlCl$.