They're not the same cannons.
The Bf.109E has the crappy Oerlikon MG/FF 20mm cannon, which has a low muzzle velocity resulting in poor trajectory, and relatively poor hitting power. Also, the MG/FF is limited to 60 rounds per gun due to the fact that it feeds from a drum magazine instead of a belt.
The Bf.109F4, like other later German aircraft, is equipped with the Mauser MG151/20, which has better hitting power and higher muzzle velocity than the MG/FF, as well as feeding from a belt meaning that you can take 200 rounds per gun instead of 60. And that's 200 rounds of more effective, easier to aim ammunition.
Couple that with the fact that the Freidrich is faster, rolls much better, is more aerodynamic (when coupled with the increased weight and engine power this means much better energy retention) and maintains control at higher speeds than the Emil, and the answer is quite clear.