Well, since minimum control speed will have been determined in near-zero crosswind, it follows that any failure which causes the crosswind to be adverse - i.e. the (most) upwind engine - will be more serious. If the wind is strong enough and the failure occurs at a critical speed and a number of other factors are (mis)aligned, then you'll be in a situation where the "minimum control speed of the day" is somewhat higher than the assumed (certification) minimum control speed and you will be lucky to avoid a runway excursion. So in terms of engine failure during the takeoff roll, the upwind engine is certainly most critical. The assumption in the text below (underlined) is that control can be maintained, and this is not assured.
during an all engine takeoff you will be holding right rudder to maintain directional control. If you had the left outboard engine fail, you’re already holding some right rudder input for the wind, you would merely need to increase the rudder you’re already holding to maintain control. On the other hand if your right outboard engine failed, you would actually need to reverse your rudder input, and this would be most dramatic just as the wheels leave the ground. Let’s also remember that it is not uncommon for winds to lift the upwind wing just as climb out begins, this would add further roll tendencies toward a failed right engine.
The dynamic effect of either engine failing at rotation will be the same (assuming that the weathercocking effect was being held) - the aircraft yaw response will be similar in magnitude. One might also assume that the wings were being kept level-ish during the roll, and the increased tendency to roll as the plane leaves the ground (and exits the ground effect of the wind) will be a "known" for the pilot, so will not be a surprise to him or her. In any case, this would have the pilot predisposed towards a into-wind roll control, which is what the upwind failure also calls for.
I'd suggest the possibilty of being unable to control the aircraft directionally outweighs any other considerations; upwind is more critical.