Oxidising power , i.e the ability to accept eelectrons for any element depends on its electron gain enthalpy as also 2 other factors:
1) Hydration energy - greater the better, which basically means that water molecules easily overcome attractive forces in the solute particles to break chemical bonds and that easy separation of solvent molecules to accommodate the solute occurs in a solution and that formation of new attractive interactions between solute and solvent particles is not that common.
Rem: sum of delta H 1, 2, and 3 is the overall enthalpy of the solution process. Rem also that H1, H2 are positive, H3 are negative...........read this up if you have forgotten.
Due to its small size Fluorine's hydration energy is very high.
2) Enthalpy of dissociation (i.e. bond dissociation energy) - lower the better
Fluoride has a greater electron-electron repulsion among the lone pairs in the small sized F2 molecule where they are much closer to each other than in case of Cl2, hence the enthalpy of dissociation of F2 is lower than Cl2.
These two results in fluorine to have a greater positive electrode potential than chlorine, which results in greater oxidising power for F2.