Which Mac Pro 5,1 (12 core) is the best to have?

Some of this has partially been answered already however…

The definitive article listing compatible CPU chips for the Mac Pro is here - https://forums.macrumors.com/threads/mac-pro-cpu-compatibility-list.1954766/

As per this list and as per previous replies the fastest original 12-core configuration was 2 x 6-core Xeon X5675 3.06GHz chips. However the fastest possible CPUs you can fit are 2 x 6-core Xeon X5690 3.46GHz chips.

When I upgraded my MacPro 2010 from 2 x 4-core 2.4GHz chips I chose to get 2 x 6-core 3.06GHz chips. This was partly to match Apple's original specs including power consumption, heat output and so on and partly that these were much cheaper than faster speed chips.

With regards to the minimum version i.e. oldest version of MacOS you can run…

According to the invaluable everymac.com website the Mac Pro 2012 3.06GHz model which was the last ever revision of the MacPro5,1 family originally shipped with MacOS 10.7.4. The same website says however that it is still capable of running MacOS 10.6 aka Snow Leopard. See https://everymac.com/systems/apple/mac_pro/specs/mac-pro-twelve-core-3.06-mid-20 12-westmere-specs.html (In reality you probably need a 10.6.4 install disc not 10.6)

The reason it can run an older version of MacOS than what it originally came with is that the only difference in hardware was the CPU speed, it was otherwise 100% identical to the Mac Pro 2010 model that preceded it and the 2010 model came with 10.6.4.

The highest 12 core configuration Apple offered was dual Xeon X5675s (3.06GHz Westmere). Those are 95 watt TDP each. Some people install X5680 or X5690, but those are 130 watt TDP and Apple never offered them. The performance between those 3 processors is very close. I chose the X5675 configuration. You should have no problem running Snow Leopard, or even Mojave (with Metal capable GPU).

Unfortunately, the last "Full Retail" snow leopard discs are 10.6.0 or possibly 10.6.3.

That Mac is said to require 10.6.5 to boot. Some Users report they can NOT Install 10.6, but can run it if it can be installed (on another qualified computer) from "Full Retail" disks and then fully software-updated to 10.6.8 which includes the old version of the Mac App Store.

The older version of the Mac App Store give you access to older versions of MacOS, so you can install something newer, like ElCapitan, which will then allow you to install a more recent version.

My 6 core Westmere 5,1 Mac Pro came with Snow Leopard, 10.6.4. It will not for any reason boot to the 10.6.3 retail disk. So that's something to keep in mind as you're looking for one of these. Make sure the seller includes the original gray disks.

Yes, it can be quite confusing to figure out some of the rules.

I suggested it might run only on the premise that drive is currently running 10.6.8, and a 5.1 Mac Pro came with 10.6.3 or 10.6.4, depending on when it was purchased. But, as you mention, the 5.1 Mac would still see those older hardware drivers and know it came from a much older Mac. Very likely, if you tried to select that drive to boot to, you'd get a NO symbol on the screen.

2010 and 2012 Mac Pro.

This is a very confusing issue, but these subtle rules apply:

A version of MacOS that is OLDER than the original-release software for a particular model Mac cannot possibly run on that Mac, because the newest drivers for its new hardware are not included. (Also, you must use release numbers, like 17E56 not just revision numbers 10.13.2 to make a completely accurate assessment.)

The instance of MacOS that "shipped in the box" with a specific computer works with that model only -- it does not have "drivers for every appropriate model Mac" so will not run on different models. Any updates you perform on that MacOS software, including re-install of the same major version, will still have only drivers for that model Mac.

--------

For Mac OS X, any version "purchased" (even for $0) and tagged with your Apple-ID will have Drivers for every appropriate model Mac. MacOS X default is to install all drivers into the system directories, and selectively load the ones needed at Startup Time.

[The Master Installer "Full Retail" CD/DVD version for purchased OS9 also contained all drivers, but the Installer default was to install for a specific Model Mac, and the option to install the bigger version with "drivers for every appropriate model Mac" was there only as an option, and difficult to access directly. So OS9 drivers were generally selected at Install-time, unless you took pains to do it the other way.]

If and only if you had started building that system with a "Full Retail" disc and the updated it, could it possibly have the required drivers.

If you started with any model-specific release disc, the newer drivers would never get added and it could not work.

If it even managed to boot to the drive from a 3,1 Mac, it very likely wouldn't run well as it would not have the necessary hardware drivers.