Having done both aikido and judo it seems to me that the two koshi-nage are quite different, in intent but perhaps not in practise.
In judo one tries to throw the partner so that he or she will land on their side in perfect breakfall position and thereby get a full point and a win. Thus nage supplies the necessary rotation. In aikido, one tries to throw the partner so that he or she will land on their face/shoulder and thereby ensure that there will not be a second attack. Thus uke supplies the rotation to land in the proper breakfall position. Of course in practise nage helps uke land safely (so one also has the option to allow an attacker to land more safely than head/shoulder impact) but one should not forget that the tecnique allows for a range of damage.