From my experience with the L925, the phone has always required a hard reset to run smoothly after every OS update.
Be it battery performance, bugginess with apps, etc, a hard reset just brings it back to its original glory...almost. And yeah, about 3 gigs of free space may help. Absolutely no issues with 8.1.1 and Denim has actually been better with battery life for my 925.
As suggested elsewhere on this forum, deleting the Cortana tile from home screen resloves the stuttering that is felt at times while exiting apps.
Even if taking a backup fails at 98%, you can rest assured that your data wont be lost while restoring. I gave up after facing that issue a number of times, but no loss of data while restoring.
If you can spend some time setting up the phone though, I think starting from scratch and restoring just the MS account, pics/videos and music is the best bet for getting a glitch free phone post the hard reset.
Good luck!