Although electron gain enthalpy of fluorine is less negative as compared to chlorine, fluorine is a stronger oxidising agent than chlorine. Why ? 

The oxidising capability of a substance can be determined by its electrode potential. Higher the electrode potential, stronger is the oxidising agent. The electrode potential, in turn, depends upon the following three factors : (i) Bond dissociation enthalpy (ii) Electron gain enthalpy and, (iii) Hydration energy. Although electron gain enthalpy of fluorine is less negative than that of chlorine but 

(a) enthalpy of dissociation of F—F bond (158.8 kJ mol^–1) is much lower than that of Cl—Cl bond (242.6 kJ mol^–1), and

(b) hydration enthalpy of F^– ion (515 kJ mol^–1) is much higher than that of Cl^– ion (381 kJ mol^–1). Because of these two reasons, electrode potential of (+ 2.87 V) is much higher than that of Cl₂ (+ 1.36 V) and hence F₂ is a stronger oxidising agent than Cl₂.