After every major update I do an FDR, even the smaller updates.
For example, I had my 2012 Wifi Nexus 7 running on 5.0.1. I had updated it to 5.1 as soon as it became available and my device was brought to a crawl in terms of performance. Opening any app was a pain and even running Clean Master before use had become part of the routine after booting it up.
I don't use my Nexus 7 as much as I used to so I decided to just do an FDR as there isn't anything important on it. The difference after was night and day, it runs smooth, apps open quickly, and I don't even have Clean Master installed on it anymore.
Yes doing an FDR is a pain, but it's the suggested remedy for a reason. New OS (well at least updated), so why not start on a clean slate?
@leeshor gave you great advice and you could try to narrow it down if you want, but if Android System is the culprit then an FDR should get your battery life back to where it used to be.
If you have any concerns about backups you can use these to help save what you want:
Photos - Google+ backup (or your SD card)
SMS/MMS - SMS Backup & Restore (save file can be emailed or to your SD card)
Any other apps you have that need info to be save (such as aCar, which I use), they can be backed up to in their programs and usually be exported to another source such as email or SD card.