I have a 4s and have iOS 9.2. As an old phone it's next to useless surfing internet, it's very slow downloading and rendering the page if it's not a mobile page. The 4s can only use weblock and not iOS 9 block functionality. Facebook, iBooks, BankID, Spotify, navigon, runkeeper, banking, messenger , mail linkedin Netflix etc. it works ok but slow opening the apps. Facebook takes ~20 seconds to fully render and update. Just timed it! When the apps are open or in the cachememory the apps works satisfying. But it's an old phone. So as a smartphone without a good webbrowser the 4s on iOS 9.2 is ok but slow.
What is an irritation in iOS 9 is it's bad registrering of finger movement on the screen, example drag finger down, touch out alarm. You will sometimes do 2-3 movements before anything happens from a locked screen. Could be that the 4s just can't keep up with the rendering of the Today screen others have been throwing out other ideas why. It's just so bad you have to stop your self throwing the phone out the window sometimes. Thinking about swiping off the alarm at the morning. Also due to the 4s slow processor typing text in mail and switching apps will sometimes not often but it happens bug out the phone stallling the text and the text takes some seconds to show after typing. You will have fun with auto spelling here. So you will notice a change here from your iOS 6, it is not snappy or fast just forget that Idea.
I have my 4s on iOS 9 as i know i will have to update to iPhone 7 this year.
Should you update? If you have the same user profile as me, using apps but not safari that is slow rendering then it's ok as a tool. Safari was almost useless on iOS 8.4.1 due to slow rendering or crashing on the 4s also so no big change change there for me. You have to tolerante or ignore the hmi bug to live with iOS 9.2. I have all standard functionality on I should state. Only a standard picture from iOS 9.2 for background and lock screen also. Siri is on but not Hey Siri. She is slow to respond if not in cache also due to her age. I updated from iOS 8.4.1 to iOS 9.2 by iTunes and using the phone the same way. I could just the same stay on OS 8.4.1 if the choice is up.
I am still on iOS 8.4 on My iPad mini 2 as i will keep it longer and will wait out further development before thinking of updating the mini 2. I use safari on it and it works fine as it is.