Just tested a K4 flown manually against auto take off. The auto pilot aircraft had about 740 yards lead when I rolled and by 28,000 ft I had closed to 300 yards. Same fuel and load.
That's close enough to say no significant performance difference but a slight edge to manual flight.
I just repeated my tests. A climb to 2000' is more realistic when having to scramble to meet incoming fighters. Here are the precise conditions used and results I got:
109K4
50% fuel load, no drop tank
standard 30mm/12mm armament load
Offline practice area, unmodified
launch direction NE
throttle initially closed
start timer when throttle goes full open
turn WEP on asap
Auto Takeoff (3 runs), time to 2000'
48 sec
46 sec
47 sec
Manual Takeoff (3 runs), time to 2000'
57 sec
58 sec
58 sec
elevator trim set to full down, adjustment made while rolling (auto takeoff does this instantly and automatically)
liftoff at 125 IAS (try to match what auto takeoff does)
climb at 135-140 IAS (try to match what auto takeoff does)
The best I could do manually was 9 seconds slower than auto, about 20% longer in time, to 2000'. I call that huge.
Btw, you noticed about a 740 yard lead on rollout using auto takeoff, right? I see about the same.
Knowing the above I will only use auto takeoff, especially when needing to scramble a fighter in a hurry.