The Cathay Pacifc style answer to this question (derived from D.P Davies' Bible, "Handling the Big Jets") is that the critical engine at or below Vr is the most outboard upwind engine because of the combined effect of assymetric thrust and weathervaning making control of the aircraft on the runway difficult.
After Vr (once airborne) the critical engine is the most outboard DOWNwind engine because of the combined effects of assymetric thrust and crosswind-induced drift making extended centreline tracking difficult.
Obstacle Clearance after take off is ensured by a surveyed, splayed area commencing at the departure end of the runway which has nothing in it which can be hit. Not tracking the centreline accurately after a critical (or any kind!) of engine failure could take you outside of this splay, where there is NO obstacle clearance guaranteed.