OK no problem. If it was the graph post that pissed you off, it was just to illustrate why the 4S is so problematic in 2016. It's actually less than 1/10th the compute power of the latest iPhone with a quarter of the RAM of current models (and 1/6th the RAM of the current Plus), so course it's going to be very slow. I didn't mean to criticize your gift though, so sorry about that.
Anyhoo, I have an iPad 2 that my very young kids use, but even they have problems with it. Basically all it can be used reliably for is Netflix and YouTube, but it lags galore for OS navigation and app switchin, and the kids wonder why the button presses sometimes don't work until a few seconds later. Surfing on it is rather painful, yet it actually has a faster CPU than the 4S. The 4S has the advantage of a smaller screen so compute requirements are less but it suffers the same problems.
If you just use it for PDA + phone, text, and NAV, and the camera, then it could work even in iOS 9, but the experience isn't really representative of iOS. The lags can be very frustrating at times. In addition to that, surfing is really, really difficult on that phone, because of the small screen size and because of the speed. In addition, there is a tendency these days for apps to crash. But if you don't surf and don't install other apps, then maybe it doesn't matter to you.
However, iOS 9 is way, way better on the iPhone 5. It's a totally different experience, even for basic use like talk and text. And it has an improved camera and more screen space for NAV too. And it can run iOS 10, but I haven't tried the 5 in iOS 10 yet. However, Ars says the iPhone 5 does well with iOS 10.
http://arstechnica.com/apple/2016/09/good-news-ios-10-runs-pretty-well-on-the-iphone-5-and-5c/
Most basic day-to-day things still feel pretty good on the iPhone 5. Bringing up the Intelligence screen, the Notification Center, the Control Center, or the multitasking switcher all happens smoothly without the inconsistency or dropped frames that plague an iPhone 4S running iOS 9. You’ll mostly run into problems in three areas: games, multitasking, and battery life.
The GPU in the iPhone 5S can be as much as three or four times faster than the GPU in the iPhone 5, and newer iPhone GPUs are even faster. That by itself is enough to explain why even simple-looking games like Pokémon Go and Shooty Skies can exhibit choppy framerates on the iPhone 5. They’re still playable, but performance is less consistent since the hardware is being pushed to its limits.
The same principle explains why multitasking—switching from one app to another, replying to a message directly from a notification, doing things with the phone while it’s also performing a background task like app updating or a large download—can make the phone chug a little. As long as you’re just doing one thing, the speed feels pretty good. The iPhone 5 launched with iOS 6, after all, software that was far more locked down and less capable than iOS is today.
And then there's battery life. Part of the problem stems from the older hardware—if the SoC is working harder than it did under older versions of iOS, that means that the chip spends less time idling, and idle time is where modern phones and laptops save power. The biggest battery life jumps in recent years have come because Apple, Intel, and others have figured out how to let their chips spend more time not doing anything and by making the processors switch between active and idle states more quickly. The iPhone 5 and 5C are working harder more often, so battery life is more of a problem than it is on a newer phone like the iPhone SE (that phone’s chips were all made using newer, more power-efficient manufacturing processes, which also helps).
The other factor is normal wear-and-tear. Any iPhone 5 or 5C out there right now is somewhere between two and four years old, and if your phone’s battery hasn’t been replaced at some point, you’ve probably lost a significant amount of capacity. Since those phones are also mostly out of warranty, it’s relatively easy to find a third-party who will change your battery out for a fresh one, and iFixit sells kits that make it relatively easy to do yourself. But if you or someone you know is using an older iPhone 5 or 5C at this point, a new battery is probably worth looking into.
The most important thing to note for the purposes of this article is that all of these things were also problems in iOS 9, and that iOS 10 doesn’t appear to make any of them worse. They’re just realities of using a phone made in 2012 to run software made in 2016. Phone hardware is maturing rapidly, but the year-over-year improvements are still noticeable, and cumulatively the last four years of updates are even more noticeable.
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To put it another way, your thresholds may be quite different than mine, but IMO the iPhone 5 is tolerable with iOS 9, and the iPhone 4S is not. And the 5S is actually fairly decent, including in iOS 10.
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