Before deciding about the wheel size of my new wheels, I tried it temporarily with ETRTO 406 wheels from another bike (but without front brake as the Birdy disc needs a special hub with the disc on the right side at a different position than the standard left side disc).
The real difference doesn't come from the wheel size but from the tires type+width.
Since you can only put narrow up to 28mm tires on the ETRTO 406 wheels and that all 28x406 tires are high pressure road tires, it rides more or less the same than similar tires on the ETRTO 355 wheel but is different from what you normally experience with the Birdy because all usual Birdy tires are much wider with lower pressure.
Te results is a faster bike, more reactive. For me the comfort is still OK due to the full suspension but others may consider it not comfortable enough.
FYI, after this test, considering that there are too few tires types possible with the ETRTO 406 wheels, I decided to mount... ETRTO 349 wheels for which there are now more tires types than in ETRTO 355 (and especially more high performances road tires).
My Birdy is equipped with Greenspeed Scorcher 120 tires inflated at 7bar which are very fast tires, as fast as the best 28x406 tires (the Schwalbe Pro-one).