The issue started after I upgraded the OS to iOS 9 (last year). The performance took a dive. I would tap on Mail app and it would take seconds before it would respond. Sometimes picking phone calls became a hit or miss, as I would tap the green answer icon and nothing would happen.
I tried many things -- reducing the level of animation, removing some apps and fiddling with a lot of settings. Nothing worked permanently.
This month I upgraded to iOS 10 and things got worse again. Now the phone will suddenly freeze and restart. Typing has now become a hard labor as the keys respond very late and generate more errors. It was pushing me towards getting another phone, if not for the new exchange rate. But yesterday I fixed it permanently.
I reset the phone. Actually, erased the iPhone. It was a bold step and it worked beautifully. I lost all my photos and movies and messages and many other things. No problem. I like new beginnings. The phone now feels like new. And works very fast and smooth. All problems gone.
Is your iPhone also giving similar problems? Well, you should try a reset. Worked great for me.