I saw many people updating their iPhone iPad to iOS 9 and suffering some problems, I'm one of them :(
I have an iPad Air and an iPhone 6. Based on the updating experience of iOS 8, I'm not sure about whether I should update to iOS 9 so early.
Finally, I tried to get iOS 9 on my iPad Air, not my iPhone, but it stuck on the Apple Logo for about 10 minutes! I googled, and found some solutions, I followed the tutorial to force reboot and put my iPad into recovery mode. It worked! And I downloaded iOS 9 via iTunes again, this time everything goes well, 15 minutes later, I have iOS 9 on my iPad now. So, if you are planning to update iOS 9, I hope this tutorial helpful for you all: http://www.imobie.com/support/common-ios-9-problems-and-solutions.htm
Good luck to you