On a jet there is no "critical engine" in the normal sense. This is a term used for twin prop aircraft where both props rotate in the same direction. All about the "downgoing blade effect"
I would suggest that in a situation where you have a significant crosswind, it would be better to lose the downwind engine, as the aircraft will have a tendency to turn towards the wind (weathercock) which you would need to counteract with rudder (I'm talking on a final approach of course, in level flight I don't think it makes any difference.) So losing the upwind engine will mean that you have less available rudder deflection to counteract the yawing effect of the good engine, as some of it is used up in counteracting the tendency to weather cock.
Of course I could be wrong, but that's my understanding of it.