I had posted a message about this a few weeks ago.
Emirates is keeping this issue very hush hush, but my understanding is that the cabin upgrade won't be launched till the A340-500 enters service. However, with the introduction of this acft being delayed consistently, you could see a surprise by Q3 2001. This is when Emirates launches very long haul services ie. PER and KIX which are 11hr+ segments. Given that many of the B777-200ERs are coming due for heavy maintenance they might squeeze the cabin upgrades on these acft then.
My understanding is that First class will get cabins similar to BA and SQ. But apparently the Emirates cabins are supposed to set new standards, and have features that BA and SQ don't. In J class, the existing F class is likely to be introduced with an outside chance of flat-beds. Y class is likely to feature more legroom given the longer segments. Finally, you will see all the other trimmings ie. new IFE (most likely to include video on demand [VOD]) and enhanced catering etc. as well as better ground services.
In terms of rollout, the new cabins were planned for the A340-500 given that these planes will do the very long stage lengths (13hr +). However, you might see the B777-200ERs get them as well since they will be doing some long stages. The rest of the fleet, ie. A330-200 and B777-200 (operating regional runs ie. the HD config acft) are likely to stay in their existing configuration.
You see Emirates current route profile hasn't seen a meaningful demand for cabins and flat-beds in premium classes because the route lengths don't extend beyond 8hrs.
Again, this is the info i have, and all is subject to change since we are a while away from launch.