In sport mode the engine responds more spontaneously to movements of the accelerator. The steering response is more direct, and with automatic transmission there is rapid gear shifting. This is normal.

It has to do partly with the Valvetronic positioning and partly engine timing. Basically the engine becomes geared more towards performance and less toward economy.
Throttle response is increased by opening the valves more through the Valvetronic system and increasing valve overlap and using more aggressive (and slightly wasteful) timing per the VANOS system.

Automatic transmission changes are the most noticeable modifications with more positive (stiffer up/down) shifting which is delayed on all accelerations (probably unchanged at full throttle though) and earlier down-shifting on all decelerations.

As for the acceleration issue, are you using less than the recommended premium fuel, or do you have check engine light? If the engine is cold, isn’t running perfect or you have low grade fuel, it protects itself by reducing performance.

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