Hi Ernst,
>In the end of the climb, when speeds falls, the airplane start to yaw.
Thinking about it, this comment might indicate that the reason you don't get the same climb rate as your opponent could be that you're climbing too slowly.
Basically, the speed for best climb rate is somewhere between "going really fast" and "hanging on the prop". If you're going too fast, it's obvious that your engine power is mainly used to going fast against high-speed drag. However, if you're going too slow, there is a lot of induced drag as the result of creating lift at a low airspeed, and that's not as obvious as the high-speed drag.
Somewhere, there is a happy medium between "too fast" and "too slow", and it's even a fairly broad airspeed range in which the climb rate is close to the optimum so you don't have to hit an exact airspeed with single-digit precision
(As a rough guideline, the real Me 109G-1 had its speed of best climb at 280 km/h IAS from sea level to full throttle height, above which it was reduced by 5 km/h IAS per kilometer of additional altitude.)
Regards,
Henning (HoHun)