Between ETRTO 406 and ETRTO 451 with the same size of tires (ETRTO 451 tires are usually narrow road tires) the difference is diameter is 45mm, i.e about 10% bigger.
But between ETRTO 355 Birdy and ETRTO 406 Birdy, because most of the ETRTO 355 tires are between 40 and 50mm while for ETRTO 406 rims the limit is about 28mm wide tire, the overall wheel size difference is smaller, i.e. between 33mm and 7mm (435mm to 455mm vs. 462mm).
When moving from ETRTO 355 to ETRTO 406, the behavior of the bike and the feeling of the rider are also changed by the move from wide mid or low pressure tires to narrow high pressure tire.