Reactivity of the element is based on the valence electrons of the atoms.
Alkali metals is part of the 1A group in the periodic table. This means that it has a valence electron of 1. It needs to expel one (1) electron to satisfy the octet rule. Also, the valence electron of the halogens which are seven (7). This means that it has to take in one last electron to satisfy the octet rule.
The reactivity differs in that the alkali metals have to expel one electron while halogens have to take in one electron.