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iOS 7 is the crappiest OS that Apple ever made, until 7.1.2. Your iPhone runs pretty fast in 7.1.2, this is clear, but iOS 9 is not far away in terms of performance.
 
The 4s has been sluggish since iOS 7.0, and that hasn't been fixed.

May as well update to 9.0.2 to enjoy the new features.
 
The 4s runs iOS 7 pretty good. You must be thinking of the 4.

With Reduce Transparency turned on, the 4s runs relatively well.

With the blur effect on, well, not so much.

I know this because I have an iPod touch 5th gen and survived iOS 7 (has the A5).
 
With Reduce Transparency turned on, the 4s runs relatively well.

With the blur effect on, well, not so much.

I know this because I have an iPod touch 5th gen and survived iOS 7 (has the A5).
The 4s was snappy and responsive, only problems were RAM and some animation stuttering. It's not laggy like on iOS 8 or 9.
 
There is another thread here:
https://forums.macrumors.com/threads/ios-annually-slowing-down-our-devices.1926081/
It is showing the difference between iOS 7 and iOS 8 on the 4S. iOS 7 is faster. There's another video in that thread showing iOS 8 vs iOS 9. iOS 8 is faster. I used an iPhone 4S on 7.1.2 recently and it performs very well. Don't upgrade unless you care more about Apple music than practically unbearable performance (compared to 7).
 
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