Except that the correspondence isn't the same every year, because leap years don't correspond (except accidentally).
The original Persian calendar started the year depending on whether the equinox was before or after noon. If before noon, that's 1 farvardin, otherwise the next day is.
Instead of 97 leap years every 400 years, the mathematical Persian calendar counts 7 leap years in a 29 year cycle or 8 leap years in a 33-year cycle (22 29-cycles and 66 33-cycles in every 88). That makes it more accurate at 365.24220 days per year than the Gregorian (365.2425), the 'real' average being 365.24219.
Still, between 1865 AD (1244 AP) and 2152 AD (1531 AP) there are only two years in which the two calendars are out of step: 2025 and 2058 AD. So it doesn't matter very much.