Which number on the rear of an original release PS2 is the proper serial number?

A PS2 contains two unique identifiers on its rear sticker. A number labeled "SERIAL" to the left, and a barcode sticker offset to the right, with different characters in each.

This random PS2 from an internet screenshot has a "serial" of "AU43211911", and a "barcode" of "PX443219113".

If I am cataloging a PS2 for asset tracking, collecting, grading, or any other purpose, which of these numbers would I use to represent its identity and why?

The actual SERIAL.

As the name says, the unique serial number in this case is AU43211911. The barcode is more of an inventory control tool.

Funnily enough, this also happens with the PS3. I have a CECH-3011A Slim console with a barcode under the console that is different than the Serial Number on the rear.