Sorry guys, but there is no koshi nage in judo. Many of the judo throws use koshi (hip throws) while others use feet, legs, shoulders...etc.
I didn't do judo for over 7 years now, so my memory is not good, but throws like ippon seoi nage, morote seoi nage, o goshi, uki goshi, harai goshi, hanae goshi...etc. are all hip throws, and they have nothing to do with our koshi nage.
The main difference I can see (which is a big difference by the way) is that aikido's koshi nage is executed at a 90 degree angle betweem nage and uke feet, while in judo, uke and tori feet and hips are usually parallel or almost parallel.
In judo, you can throw an unwilling person using a hip throw (even if he's pulling backwards, while in aikido nage should be using uke's movement otherwise it would be more difficult to execute.