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.