As a Qantas WP (and former CX DM), I always fly J with CX MEL-HKG so no chance of an op-up, but I know how the DM's are treated.
Normally, I go straight to sleep since I've already eaten better in the QF 1st lounge than I could expect to onboard CX in J.
The one time I actually had dinner on the flight, I received the little welcome card written by the FA's - as is usual for a DM. They even wrote: As a Diamond member, etc. etc.
Maybe they are all pre-written and they just added the name, but the fact that I'm not a DM any more and had checked-in using my QF WP FF number, I thought that was pretty special.
It also made me realise that Platinum / Diamond on QF or CX are pretty interchangable these days - so it's not worth the effort to try and maintain that level of status with both of them.