It could be that Spotlight is still indexing, or it's doing some other stuff in the background. It can also be that it needs to purge installation files, which might be difficult if the device is pretty much filled up. Do you have a vast amount of free space, like > 20%? I did when upgrading an iPad3 earlier today and in spite of many negative posts on the Internet this iPad3 (March 2012) is doing very well. No lag, not faster, but everything works. Plus all new goodies (well, expect for Handoff and such).
But ok, that was an iPad. Now just finished upgrading an iPhone5 (2012) which had 27GB free. Installation was quick, with USB <> iTunes and downloading the 1.78GB iPhone5,2_8.0_12A365_Restore.ipsw. Reboot, apps are quick, but you will see a delay on some when opening them for the 1st time. So do that, and close all apps, do a reboot and use the phone for a few hours. See is Safari is still slow, experience the whole thing. If you don't like it I suggest you rollback to iOS7 because it's expected that Apple will discontinue signing iOS7 tomorrow.
Best