Mac Pro (late 2013) SSD Upgrade

Taking some of those values quite literally, x4 slot is four bits wide (actually 4 one-bit serial streams wide, but it works out to the same thing).

5.0G Transfers/sec means that you can theoretically transfer 2.5 GigaBytes/sec, or 2,500 MegaBytes/sec. Each byte of data is 8bit/10bit encoded, which drops the rate closer to 2,000 M Bytes /second, and overhead and drive latency leaves you with a nominal 1500 M Bytes/sec, which is about what you measured.

You MUST upgrade your Mac to be running High Sierra or later BEFORE you attempt any swap. The last version of High Sierra installs a firmware update (stored in the firmware store on the processor card, not on any drive) that enables 'regular' NVMe drives to be used with adapter, or certain OWC drives directly.

 menu >about this Mac > (system Report) > PCIe slot ...

the two last lines will be:

Link Width: {x1, x4, x8, x16}

Link Speed: {2.5GT/s, 5.0GT/s, 10GT/s}

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My guess is that those will be x4 and 5.0GT/sec [PCIe 2.0], which corresponds perfectly to your tested speed of around 1500 M Bytes/sec.

This is confirmed by EveryMac.com:

Instead, the Cylinder Mac Pro models have only one internal "blade" SSD. Specifically, the SSD uses a custom Apple design with a PCIe 2.0 x4 interface, which is capable of a theoretical maximum speed of 2 GB/s.

from:

https://everymac.com/systems/apple/mac_pro/mac-pro-cylinder-faq/how-to-upgrade-mac-pro-cylinder-ssd-storage.html

You can't run a really fast drive on a much slower bus and get any better performance that what the bus supports. In 2013 when that Mac was issued, those speeds were very impressive.

<< do you think OWC drives would perform better or any other drive at all or does Mac Pro disk speed peaks at 1300MB/1400MB? >>

No drive can do better because the limiting factor is the SLOT, not the drive.

the report you posted is showing the speed for one of the two graphics card slots. Look further down the list and you may find your drive, or perhaps it is on the NVMExpress pane.

External drives will also be limited to the Thunderbolt equivalent of an x4 slot, and perform at about the same about 1500-ish M Bytes/sec level.

A newer Mac Pro with PCIe-3 slots, or any Mac with wider PCIe Slots could have faster transfers.

RAID sounds great, but its payback using already low-latency SSD drives is very small, and it has the same speed limits as any Thunderbolt device.

Absolutely NOT worth the money.

ThunderBolt-2 and 3 are overall speed is limited to the equivalent of an x4 PCIe 2.0 slot and can not possibly test better than about 1500-ish M Bytes/sec you are currently getting, no matter how much expensive and complicated hardware you hang off it.