Let's consider a take-off with a crosswind from the left. The wind will try to force the fin to the right, and therefore the pilot will apply right rudder to keep the aircraft straight. If the left (upwind0) engine fails at V1, then the pilot must apply even more right rudder to keep the aircraft straight until Vr. As the V1 must always be equal to, or above Vmcg, then this should be OK, but on aircraft such as the B747, Vmcg is calculated with a maximum crosswind of 7 knots (Vmcg has been covered on previous threads). Therfore between V1 and Vr an upwind failure is the most critical.
However, once airbourne, the limitations of Vmca become predominent. Immmediately after rotate, the pilot will still be applying right rudder and left aileron. Now, a failure of the right engine will require him to transition from right rudder to left rudder, at the same time keeping the wings level with the ailerons. A failure of the left engine will only require an increase in the already applied right redder, once again keeping the wings level with the ailerons.
So it can be seen that between V1 and Vr, the upwind engine is the most critical, and immediately after Vr, the downwind engine is the most critical. As Vmca is generally less than Vmcg, then the case between V1 and Vr is the most critical. Of course once the rotation is complete, and the 'crossed controls' are neutralised, it makes no diference which engine fails.