This is how i see it.
Crosswind take off (both engines). You need rudder to head straight ahead. If you keep this rudder you will track to one side after take off. So you relax and use NO rudder.
Crosswind take off (engine fail). You still want to TRACK ahead. So you still want to weathercock to one side. You use the rudder to prevent it going left / right of the weathercocked hdg.
Therefore there is no preference which side fails, you will need no more / less rudder, as if you use the same amount as normal, the a/c will weather cock - what you want it to do.
Ok ?
