Re: Franco Kernel, my experience
I'd say Google does an okay job with their kernel which actually have minimum cpu speed lock at 900mhz, it have a good compromise between speed and battery life, except for the ridiculous low cpu temperature throttling. It really depends on your settings, someone with the same setup could get bad battery life. I can't imagine getting 5hrs if I play games or do intensive tasks.
I get 4hrs of battery life with stock kernel, but I remove most junk apps and use Greenify. The thing Google need to fix is more on the OS, like tissues with wakelock and background processes eating battery, doesn't matter what Android forum you're in, this topic pops up.
Since you have franco kernel, I recommend installing TouchControl to enable swipe2wake and sleep module if you haven't tried that, it will embarress the LG G2. Some kernels have the feature built-in, but out of all of them most have issues with the touchscreen becoming unreponsive forever and had to reboot, there is only one kernel for the N4 I know this without the bug.
You should try TricksterMOD if you haven't, it's one of the best app for changing kernel settings.