I agree the two are very nearly identical, and could often be used interchangably. I would say the subtle difference mostly concerns the object that is being emphasized, either "the birthday" or the implied "it".

"It" likely refers to a particular day -- yesterday, last Tuesday, etc. Someone might ask, "What was special about yesterday", to which you might reply "It (the day) was my birthday".

In contrast "My birthday was yesterday" put the focus on the event itself. Someone might ask "When was your birthday", to which you might answer "My birthday (it) was yesterday".

Subtle.

I agree the two are very nearly identical, and could often be used interchangably. I would say the subtle difference mostly concerns the object that is being emphasized, either "the birthday" or the implied "it".

"It" likely refers to a particular day — yesterday, last Tuesday, etc. Someone might ask, "What was special about yesterday", to which you might reply "It (the day) was my birthday".

In contrast "My birthday was yesterday" puts the focus on the event itself. Someone might ask "When was your birthday", to which you might answer "My birthday (it) was yesterday".

Subtle.