besides the fallacy that HP) is ready to use sooner, I've found that the soaps are not different than CP that is gelled. and the diff between gelled and ungelled is small.
The way it looks is probably the biggest difference. HP is rougher and more textured versus the smooth creamy look of CP. HP is great if you just have to use an FO that seizes in your CP soap. I'm going to do an HP this week with an FO that faded in my CP soap and see if it will stick.