iOS 10 released a couple of days ago and soon after iPhone users started downloading it, it turned out that a lot of their phones got bricked soon after the installation was completed. Before things got out of hand, Apple released a quick fix to sort out the issue but complaints of existing iPhones running slower than usual haven't really died down.
A reason for this could be the fact that iOS 10 is taking its own sweet time to integrate with apps, merge with tools and get things in order for an iPhone to run the way the latest OS has been designed to increase speed, conserve power etc. This may take some time and will consequently take a toll on an iPhone's processing power until things get straightened out. It is possible that a number of users may not have installed the fix that Apple sent out over the air to kill the bug that arrived with iOS 10.
A lot of apps may also malfunction or slow down if their developers haven't optimised them to work with iOS 10 as yet. While Apple's pre-installed apps won't face such issues, a number of third party apps which need to obtain information about an iPhone's hardware or software may malfunction. These may include battery saving apps, antivirus apps and ad blocking apps and so on.
Since iOS 10 is new and quite raw as of now, it is possible that more bugs may be discovered in the coming days. Apple will surely issue fixes once new bugs are discovered, but existing iPhone owners will need to be patient for a few days to let their iPhones and the new operating system to get to know each other better.