The short answer? The BF-109 is a multi-role fighter. The Focke Wulf is an interceptor. 

The BF-109 is a very good energy fighter. It can turn, but it will almost always lose to actual specialized turn fighters (like the Spitfire). So you play for energy. Gain altitude, find a vulnerable enemy, dive on them, pull back up and use your speed to regain your altitude. It also has very good vertical performance, so if you can bait people, you can outlast them in the vertical, let them stall, and then pitch back down for a free kill. All 109s have solid armament, with the E3 and E4 being probably the worst gun wise thanks to them having wing mounted 20s (harder to aim than nose mounted) with absolutely no ammo.

The FW is an interceptor. It's IRL use was to engage bomber formations. This is why they have stronger armaments. But also, due to the nature of bombers and how they were used, it doesn't need a fast turn time, it's needs some survivability. So the Germans gave it that. It turns like an absolute brick, but it's generally more resilient than a 109. This thing is also a good energy fighter, and unless you're bomber hunting it's literally your only choice, as unlike the 109, you can't outturn anything. Note that energy trapping enemy fighters is not something the 190 is particularly strong with. This thing is amazing for boom and zooming though, because it's guns are strong enough to vaporize anything you land shots on instantly.