I'm with JohnAx on this one.
One example: If I do HKG-xLAX-SCL I get nearly 24hrs to rest and sleep at a LAX hotel, so by the time I get to SCL I'm in top shape, yet if I do it the other way around I get a few hours at the LAX lounge and that's it; by the time I get to HKG I'm a wreck. Another example, but in reverse: LHR-xLAX-SCL.
More than once I have selected the direction of travel just for this reason.