The most stable custom ROM I've tried is Unofficial CyanogenMod 12.1 which is based on Lollipop 5.1.1 ported by Team Canjica from XDA Dev. I have no big issues and problems for my daily use, although I have to lose some Touchwiz features like Air Gesture or Air View, but who cares with that gimmick function that I never use.
Battery consumption so far is fair for Lollipop system, you can see the screenshot of the state below this post.
Here's the link to download
Unofficial CM12.1 Team Canjica Lollipop 5.1.1 for Samsung Galaxy S4 (I9500)
You can read the original thread on XDA on how to install and another stuff that you may need.