I have done a 1.6 to 2.0 swap, the reverse is about the same.
As it is a 147 they all use the ME7.3.1 ECU, so you just need to swap the engine and ecu (and code ecu and keys).
The electrical system is the same in the two versions, only in the 1.6 there isn't a VIM manifold plug.
All the sensors are the same, so it's up to you to keep the 2.0 ones or fit the 1.6 ones.
You don't need to fit the variable intake manifold from the 2.0, because the 1.6 ecu doesn't control it.
The twin cat section of the exaust seems to be a little longer in the 2.0 engine (bigger bottom end), so you may not be able to fit the bracket that holds it to the 1.6's block. You can leave it out, though.
I kept the twin cat pipes from the 1.6 to the 2.0 and it is a bit short, staying very near to the engine's block and not beeing able to fit the support bracket.
I also kept the 1.6 gearbox as it makes the 2.0 a bit faster, but I don't know how the 1.6 would cope with the 2.0 box... Best to also swap the gearbox.
Alfa 156 SW 2.0 TS (former 1.6 TS)