I'm experiencing the exact same issues. Stack + backboardd in the logs and my 5s standby is the same as prior to 8 but battery drops much more quickly when actually using the phone. Pondered doing a clean install but it looks like it may not be of any use. It's also happening to my rMini but with the addition of tons of "JetsamEvent" entries in the diagnostic logs.
Bizarre still is how my iPad Air with GM also has the backboardd process error logs, but excellent battery life. After a full charge while installing, its now been 11 days of reading/browsing (2-3 hours per day) and it's got 55% battery remaining. The 5s on the other hand has rapid battery depletion only during use, as you described.
If there ever were a phantom bug......