Thread title seems like an invitation to a religious war.
But I'll plunge in anyway.
1)Battery drain can be due to so many things, I wouldn't assume kernel. More likely an app or a setting. Install a good battery stats app and learn how to interpret the results.
Sometimes reinstalling the entire ROM won't even help. Flash back to a Sense ROM and see if you still have bad battery life. If so it could be firmware/radios etc.
Google, for better or for worse, controls every aspect of a Nexus or GPE ROM. They have vast resources. They have talent, discipline, and access to low level hardware drivers etc. These ROMs come loaded with the whole arsenal of Google apps and are intended to showcase an optimized Google "experience"
AOSP ROMs , even Cyanogen, are produced by amateurs that do not have the same resources. They do amazing work, but necessarily they are going to take much longer to get up to speed after major changes to Android. Also, Google apps are not even included, technically. And cyanogen in particular has created their own control panels, apps, over-the-air update schemesand other proprietary systems that have nothing to do with Google.
If you are looking for purity, the question is "pure what"? Pure Google? Go with GPE.
Pure Freedom from Google? A pure, non-corporate, best-effort attempt at compiling a functioning ROM using the AOSP programming environment? Go with CM.
Google controls AOSP, admittedly, but they have no control over what projects others produce using it.
Sent from my HTC One using xda app-developers app