It depends how different the compressor curves are for the 2 units, but generally speaking a remap is advised for both fuelling reasons, and to get the best performance.
The way I see it:
The ECU uses the MAF sensor to determine engine load on boost, and the ECU contains fuelling maps / lookup tables for a given MAF voltage. If you put a different type turbo on there, the actual boost and volumetric flow will be different to the stock map, and therefore the fuelling may well be off - causing a different AFR. As the ECU ignores the lambda when on boost, you have nowt looking at fuelling other than from a secondary point of view via the knock control.
You are then relying on the knock control from the knock sensor and ECU to adjust your timing, so if its running lean it might pick up knock and back off timing etc - but not very optimum performance wise.