I am 99.9% certain it is a BMW unit. I think, but am less certain, it is out of the 130 Coupe.
As Martin says, given the mounting, any Caterham diff will not be silent. However it shouldnt drown out the engine ! Mine did, and I have taken it to Road & Race where they are working their magic.
TBH, although I havent received the letter (yet, and maybe I wont - my car is three years old) I would still go down the R&R route to fix a noisy diff. To me, a new diff, for which the chassis was not originally designed, is a step too far away from the original car for my liking, especially as it adds weight (I assume).
I accept that others will have a different view, and some others may be put off by considerations of cost, or weight.
Angus