If you want to use this phone till it's full potential, you need to spend a lot more time studying... not just a normal consumer phone

Smart people that done enough research end up buying nexus 4.. Hehe

Your name remind me of Maple Story lol

Btw, you can play with stock for few weeks. After bored and know what you are doing with root then you can start exploring 

I am still on stock ROM! seriously, best in stability and smoothness.

Rooted my phone once i got it out of the box, custom ROM the next day 

Me straight unlock,root,flash already on first day 

if you charge your phone on daily basis, even stock kernel and rom should be good enough.

quad core technically consume more, so starting with NVidia Tegra 3 (first quad core CPU for mobile), kernel already implement auto_hotplug which allow kernel to decide to use only more core when needed.

qualcomm's S4 pro implement it slightly differently using mpdecision - a userland process that something similar. however, since it's not open source, many custom developers decided to removed that and implement the hotplug.

so, even in stock kernel and ROM, it's not that bad.

all stock ROM are using OnDemand CPU governor. in term of power saving this CPU governor is second only to Powersave and sometimes Conservative. most custom ROM using Interactive which may make the phone more responsible, but cannot match the power saving of OnDemand. (On side note, Interactive CPU Governor may not be best for Nexus 4 or any Jellybean android since Project Butter is more effective than CPU governor. it will automatically boost CPU freq on touch.)

there are other settings such as larger data buffering, low memory killer settings, io scheduler, etc that custom ROM may implement to conserve power, but in my testing, they are soooo minor. so custom ROM offer little in power saving nowadays.

custom kernel offers more nowadays. with custom kernel, you can do under-volting. typically allow your CPU to run at same speed (or higher) at lower voltage. other than that, you also can implement lower lowest brightness etc.

although i m still using Stock ROM (with some customization), i m using a custom kernel for power saving and lower heat. ohh... ya, custom kernel allow me to calibrate Nexus 4 screen too, which LG and Google really do not do justice for the IPS screen.

must be gps or sync running background or some hidden apps running background. Root it and try Greenify(apps) those unwanted running background apps.