I had horrible batter drain initially, but disabled a few things and now my battery life is back where it was prior to the 8.1 upgrade
1- Location services ON, but most individual apps I've set to not able to use it.
2- Cortana is ON
3- WIFI is ON, but WIFI sense is OFF
4- Sync Settings (themes, favorites, etc.) off.
5- Email accounts were deleted and then re-added with sync at every 30 minutes for 7 days of mail
6- Battery Saver is OFF - This was the single biggest drain on my battery. Even Battery Saver listed itself as the #1 drain on the battery
I've had a couple of instances where the phone starts to heat up like crazy and gets stuck in the "Loading...." screen when I hit the power button. All I've had to do is turn the phone off and back on to resolve this.
As time goes on the battery life and phone stability seem to be improving (no idea how that'd work).
Even with pretty moderate usage throughout the day (Weave News - a big drainer, lots of texting, weather, sports, some Cortana, Nokia Mix Radio) I am finishing my day (from 7am to Midnight) around 50% battery.
It was horrible at first, but this is completely acceptable now. More than I need to get through the day on my Lumia Icon.