Compared to iOS 8, iOS 10 seems to need about 300MB to 900MB of additional space. On the other hand, if your iPhone has automatically downloaded the iOS 10 installer, installing it will free up the space it is taking up. On my own iPhone, the installer is about 1.1GB. You may or may not have manually removed the installer (which is possible on iOS 9, I don’t remember whether it was on iOS 8). Depending on that, you will either gain some free space, or might lose quite some of it.
The Ars Technica review article on iOS 9 said:
With just a handful of exceptions, iOS 9 isn't going to give you space back, but, even when it does consume more space than iOS 8.4, its impact is negligible. You rarely lose more than 100 or 200MB.
And, in comparing with iOS 9, the Ars Technica review article on iOS 10 says:
Once you convert the numbers to reflect the way iOS 10 reports storage capacity, what looked like an increase in available space is revealed to be a slight decrease. Usually it's somewhere between 200 and 700 megabytes, a drop in the bucket on a 64GB-and-up phone or tablet but a more significant fraction of a 16GB device's precious free space.
So combined, and with some exceptions, iOS 10 needs about 100MB+200MB to 200B+700MB of additional space compared to its two predecessors.
Note that the iOS 10 review article mentions storage is now reported in base 10 rather than base 2, the article explains the details and how this was taken into account when comparing iOS 10 to iOS 9. (I’m afraid the above is mixing and adding base 2 and base 10 numbers, but the numbers are small enough for this not to matter much.)