Compare the oxidizing action of F2 and Cl2 by considering parameters such as bond dissociation enthalpy, electron gain enthalpy and hydration enthalpy.
Although electron gain enthalpy of fluorine is less than that of chlorine because of the small size of fluorine, but the oxidising power depends on other factors like bond dissociation energy and hydration energy. The smaller the size of the atom, the greater the hydration enthalpy. Fluorine being small in size has higher hydration enthalpy as compared to chlorine.
Also, fluorine faces greater inter-electronic repulsion among its lone pairs of electrons because of its small size, while there is very less repulsion in chlorine. Hence, the bond dissociation enthalpy of fluorine is lower than that of chlorine.
Thus, the high hydration enthalpy and low bond dissociation enthalpy of fluorine result in its higher oxidising power as compared to that of chlorine.