iOS 9 and iOS 8 size difference
The space needed to download the first part of the installer was optimized. It's possible to engineer for any number of trade offs - in this case, work was done to reduce the footprint of the download. 

I haven't reverse engineered the installer, but my hunch is that iOS 8 added new features to allow better cleaning and update hooks so this is more a feature of iOS 8 which runs the new installer than 9 being so much smaller. I'm sure 9 is somewhat smaller, but this is a big jump as you have noticed.