If the N-S is more desirable, then why? We have never been on a river cruise before.
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You start in Amsterdam, which is a good place to fly in a day early, but since so many cruises start or visit there not a place you need many days on any particular trip.+1. The ease of spending a night in Amsterdam to overcome jetlag, with no pressure to do more than light sightseeing, was one reason we chose A->B.
Going south on the Rhine is sailing upstream and requires more fuel. Sailing north is faster and allows more time for docks and/or excursions.This is true, and it is the answer to the OP's question about the price difference. We never felt rushed going N->S, but if you want to maximize docking time, pick S->N.