So I've taken the liberty to run five different setups, (I can take some more as requests, if necessary.) and ran A LOT of benchmarks between all of them to see which ROM provides the best performance. These tests include four various games, some synthetic benchmarks, and storage tests. At the end of it all, I ran all the tests with some pretty heavy kernel based performance modifications that gave a surprising amount of performance gains in some scenarios.
The ROM setups I am using are:
Completely Stock (OOS Beta 11 with zero modifications)
Stock OOS Beta 11 but Magisk / xXx NoLimits xXx 10.1 / Data Formatted as F2FS
HavocOS 3.3 Build 3/17 w/ F2FS
Paranoid Android Quartz Beta 5 w/ F2FS
& Paranoid Android Quartz Beta 5 w/ F2FS AND SmurfKernel 3.5.1 rc17 slmk w/ Overclocks Enabled
All benchmarks were ran under the scrcpy ADB screen mirroring software, and under the settings I've used, it's shown to not provide any amount of performance loss. The command/options I've ran are "scrcpy --render-expired-frames -b 2M -m 768". That makes scrcpy not drop any lost frames (which will increase delay but make frame rate recording much more accurate), have a bitrate of 2Mbit/s, and have a screen height of only 768, which is easy for the phone to do while not incurring any performance loss. Game performance was recorded using MSI Afterburner over the scrcpy window, which isn't THE MOST accurate, but is the only option available due to certain apps not being able to be run under OOS (i.e. KFMARK actually offers these features in app, but crashes on OOS.)
So, lets get started, first, with the gaming benchmarks. I've chosen these games because they are the only ones that are intensive enough on the phone's hardware that can run without hitting the game's frame rate cap. The overclocking kernel of choice for these tests are @pappaschlumpf's SmurfKernel, all my settings can be found here.
So, what is the takeaway from all this? Which is the winner of the best performing ROM? I think the short answer is, well, no one. Long answer? It really depends. Currently, I don't think ROMs alone can offer any amount of increase in CPU/GPU, giving any extra gaming performance. That seems to be solely up to the kernel.
At a glance, it may look like Havoc offers an immense increase in gaming performance from looking at all of the benchmarks. However, after checking Kernel Tuner, I actually noticed its kernel overclocks the GPU to 675 MHz, (up from 585).
Strangely, OOS seems to offer better SQLite performance than both other ROMs until some serious kernel tweaking is introduced. It may look like xXx NoLimits xXx gives higher storage based scores, but the gains were due to /data being formatted to F2FS. Thus, it seems like NoLimits provides zero recordable performance difference. Not sure what they mean by Speed/RAM optimized. Maybe it's just purely a debloating and keep-more-apps-in-Ram tool.
CPU scores between all ROMs is all within margin of error. I noticed higher MEM/Storage benchmark scores on AOSPA, as well as slightly faster app install times. However I imagine that comes from the fact that it uses the @arter97 kernel, not due to the ROM itself.
So, with all this said, I think the best ROM to choose is whichever one you feel like has the best features / ability to be a daily driver, not what you think will be better performance. I am personally sticking with Paranoid Android because some others have one or two annoying bugs that they haven't squashed and apps like Reachability Cursor and KFMark work seamlessly on it (unlike OOS).