Have things changed with regards to the BA sleeper service? I wasn't aware that it was in First at all, although portions if it are offered anyways on all flights. I also didn't realize that in Club passengers could have a full meal service, I thought only the express meal was served on board.

I think it is something that EK should consider, and they likely have. But the BA service is best designed for short TATLs where people are likely to work the whole next day in London. Lots of EK passengers will have another long flight after they arrive in DXB, so there is less need to get every extra minute of sleep.