In group 1 elements (alkali metals) the reactivity of the metals is mainly due to the electron releasing tendency of their atoms, which is related to ionization enthalpy, Since ionization, enthalpy decreases down the group, the reactivity of alkali metals increases.
In group 17 elements (halogens), the reactivity is linked with an electron accepting tendency of the members of the family. It is linked with electronegativity and electron gain enthalpy. Since both of them decrease down the group, the reactivity therefore decreases.
