The engines and ECU'S are the same, it's just the mapping that is different. I have spoken to a several people that provide remaps in the UK and they all said the same - after remap it will achieve same figures for remap of a 250.
The tuning boxes don't as they are affecting the existing state of tune. So a 220 with a tuning box will be down on a 250 with the same tuning box. However, it is possible to close the gap by using one of the tuning boxes that also increase boost, as you can run a higher setting on the 220 vs the 250 without tripping overboost and limp mode. It appears that MB have achieved most of the 250 gains by increasing boost pressure over the 220.
Cheers
Steve