I am typing this from an iPad 4 running iOS 10.
It is fine. Not as snappy as My iPhone 7 or iPhone 6s, but fine. In fact since the video card died on my iMac the ipad4 is my home computer. Yes it has its limitations, but I will put up with it until I see what the new iMacs are like, before making a decision on moving to the dark side after over thirty years of macs.
I suspect your concern is the experience of an iPad 2 and upgraded iOSs. We have one of those too and performance on ios9 is glacial. The ipad4 with iOS 10 is nothing like that. There is an occasional pause, but only occasionally. Otherwise it works well.
As to trying the upgrade on the device rather than via iTunes, I reckon it is such a big upgrade (figuratively, not literally) you really should back up and then restore the device so everything is optimised, although I suspect that isnt the right word. You should back up anyway just in case things go pearshaped. Then the capacity issue will not be a problem, and it is all clean and sparkly.