[Galaxy Note GT-N7000 Original Android Development] scourgeofgod:
Summary of Kernels - Updated 21/07/12

^^ As such there is no single commonly acknowledged "best" kernel for Paranoid Android.

But i can list the choice available currently.

1)Kernel_CM9_RC2_20120719_CWM_Flashable

The recovery is updated to latest version - CWMR 6.0.0.2, without the lag found in previous 5.5.x.x bundled with CM9 till now.Moreover performing a Nandroid backup is now super fast and is only 30-35mb large!, for a ROM which already has one fullbackup. It may also incorporate the 5.6.x.x protection of chainfire in recovery against emmc bug (maybe redundant in this case as CM9 already has protection against it).Finally its the release candidate 2 (RC2), so we can generally expect improvements in kernel characteristics compared to the bundled kernel of PA 0.5 (AFAIK its based on 10/7 nightly). This is assuming Imilka has not made any PA specific modifications to the bundled kernel to go along with the PA ROM - but this has to be confirmed.

2)AniDroid (links below)

This a version of CM9 kernel which supports Overclocking by NovicDev.It is super snappy and fast (quadrant scores maynot always show this). However, apps cannot be installed on SD card on this kernel(yet) - (imo, this is not a big nag as Note has lot of RAM). But this kernel is new and holds a lot of promise in its future iterations.

AniDroid v5

AniDroid v4

3)Asylum BBQ Kernels

This is a variation of AniDroid v4 - it has been optimised for framework of Asylum ROM - its fast and snappy with good battery life on Asylum ROM. No one reported its effects on PA 0.5. But i think it doesnt have the SD card installation problem of AniDroid.

Asylum BBQ v19 - Based on CM9RC2

Asylum BBQ v18 - Based on Anidroid v4

4)Old CM9 Nightlies (links below) - as with all development, bugfixes frequently tend to break code somewhere else - so improvement is definitely palpable over long periods but is not guaranteed in immediate iterations. So if your latest kernel update has broken your previous good functionality (wifi,gps,battery etc) you can revert to an older kernel. However this zeroing onto the kernel which works for you is a trial and error process completely.

Kernel_CM9_20120707_CWM_Flashable

Kernel_CM9_20120708_CWM_Flashable

Kernel_CM9_20120709_CWM_Flashable

Kernel_CM9_20120710_CWM_Flashable

Kernel_CM9_20120712_CWM_Flashable

Kernel_CM9_20120715_CWM_Flashable

Kernel_CM9_20120717_CWM_Flashable

Kernel_CM9_20120721_CWM_Flashable - Recovery updated to 6.0.1.0 CWM

5)Thor kernel v17 - it is a Kangbanged kernel (i.e palgarised from various sources without acknowledging the original devs - it is not opensource so you cant be sure of your privacy - your confidential passwords may get pasted over the net ! - lol) ,however it supports OC . Another nag with it is it has a "Thor" customrecovery bundled with it - its compatiability and performance with previous nandroid backups is unknown. IMO AniDroid kernel is as good if not better. Only advantage of Thor is that its latest iteration incorporates some form of Spen offset correction - which is a novel feature and deserves appreciation. Iam not going to link to it as its against xda rules.

6)Bundled Kernels

After flashing one of the above if you want to revert back to the kernel originally bundled with your PA rom you can choose it below(incase you dont have a nandroid backup).

ParanoidDroid kernel v0.5

Staxxtanium 1.6aF

Quick walkthrough on flashing kernels

1)Backup your ROM.

2)Flash Jbroid Kernel cleaning script.

3)Wipe Cache

4)Wipe Dalvik

5)Flash Kernel.

Edit: Special Thanks goes to Chasmodo for extracting and linking up most of the kernels. Dont forget to thank him in one of his ubiquitous posts for this.