Mine has also been going downhill ever since 6.1.3. I just did a full restore as new, no backing up and it really hasn't made a difference. Waiting patiently for the next update will be the only way to really solve my issue I think.
What do you have your brightness set to? What apps do you have in notification center? What apps are using location services? How many mail accounts are setup and how often are they set to fetch, any set to push? And lastly; do you have FaceBook app installed and if so, in settings within the app itself what apps are using push notification?
Settings > iCloud. Make sure everything you want saved is on. Then make a back up. Proceed with a restore. Start the phone as new, log in with your Apple ID. It will then ask you if you want to restore from an iCloud back. It will likely list 2 entries with dates they were made. Use the one you just did and let it do its thing, the phone will (should) look identical to how it was when the back was made. The process takes a while downloading apps, photos, etc etc.
I restore every 6 months because I find iOS gets slow and this fixes it. Plus you gain some same back on the internal memory.