Not sure on the battery life in this phone as I didn't even let the initial charge die before flashing, but it feels much faster when opening apps and switching between them. Part of it is there is less overhead running in the system, part of it is some of the performance portions of CM10.1 are optimized for the S4 chip over the Samsung software.
Some of the software is more minimalistic than the Samsung versions (which also helps with some of the speed) but I came from a Galaxy Nexus with CM9, CM10, and then CM10.1 and before that was a HTC Inspire with CM7 and I personally prefer the stock Android or the CM upgrades to stock over Touchwiz. The nice thing is you can always take a Nandroid backup of the stock setup and always go back if you find CM isn't for you.