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No chance, and that is not because of the types of aircraft used but how they were used. The Luftwaffe's tactics, organisation, communications and intelligence were not up to the task, just to mention some of the problems.
You do have a point on this
Goering thought in 1945 that the Bob had been fought to a draw, as do many modern historians. That is not what the surviving Luftwaffe pilots thought at the time. They felt they had been beaten. Having a different aircraft (if DB powered this means fewer of the other two principal types) would not have altered that.
LW was given a Mission and failed to complete it. Defeat. Fw 187 could ,with proper tactis, have made the result much more costly for the england
The Fw 187 would not have outclassed the British fighters. It might have drawn squadrons outside 11 Group into the battle by dint of its superior range. That would have made Leigh-Mallory, Bader and the rest of 12 Group happy men.
A single Seat DB601 Fw 187 would have outclass the hurricain and would have a clear edge on spitfire. This particular discussion has been made extensively in the past. We dont agree, it s ok
Cheers
Steve