UPDATE: Today,Oct 2 2015 iOS 9.0.2 was released , udpate it.
I have read reports that iOS 9 update failed for many users around the world. However for me it worked like a charm. You need to have storage space of atleast 1 GB before the upgrade. The phone should be plugged into power .
The main differences observed on my iPhone 5 are better battery life, a new system font, improved Siri, notes app, more improved search app which doubles up as a calculator
Enable Low Power Mode to save battery once the level goes down say 30 pct