My 1520 was slow to start with but after a few days it was fine and made my battery last 20% longer with heavy use, and other 1520 users say the same that I have seen. I did do a few hard resets for other reasons. If that made a difference I wouldn't know but give it a few days and it may be worth to drain your battery to 0% just to recalibrate it. But after a few days it will be back to normal.
I would agree with switch here, sometimes phones just need to recalibrate but it's mostly for batteries and not for performance.
My Nexus 5's battery got better after extended use.(others have also reported this)
But as far as performance goes, I tried Windows Phone 8(Black) and 8.1(Cyan) on the 520, it did impact performance quite a bit but was still usable.
Considering that the 920 has more powerful hardware you might experience some slow downs every now and then but 8.1 will run smoothly most times.
I hope the next thing to do with Windows Phone for Microsoft is to add performance improvements because recent updates have somewhat degraded performance.
But I talked to some developers of Windows Phone( I was planning to become one myself) and the developers said that the UI has become a bit slower in 8.1 but the apps will get faster, due to a kernel update.