Answer:
In principle, the same formulas are used for the calculation of Mcr. Nevertheless, there is a big difference:
DIN 8800‑2 simplifies the coefficient of load application point C₂ and sets it to 0.5. Eurocode 3 describes this coefficient more precisely. Depending on the load action, C₂ can be between 0.41 and 1.562.
If the load application point is placed in the center of gravity (provided that the cross-section is double-symmetric), the Mcr values are the same according to DIN 18800 and EC 3.