My differential makes a whining noise on tight turns and a little bit when reversing (wheel bearings and universal joints are good).

Now I have (dis)assembled a number of rear axles for an X308, but I have never seen a green sticker with a part number (which now makes noise under my XJR)

The part number reads JLM20494 (E?) and according to a quick google search this is a 3.06 differential.
There is a post on this forum explaining the meaning of the colored stickers and what gear ratio goes with them, but none of them are as low as 3.06 (or even close).

What kind of differential do I have? Is this a special thing or normal under an XJR?

See image below:

It's hard to read in the picture, but the sticker says "Genuine exchange product ...company name?... JLM 20494 E"

 

Every single X308 ever made from the factory has a 3.06 14HU open differential.

 

In the US anyway. I think the 3.2 ROWs got a 3.27 or something

 

I completely forgot about that Quad, good catch!

 

Any part number with an 'E' suffix is an EXCHANGE unit.