My British passport says I was born in Birr; my Irish passport says I was born in Galway. These are both correct, because they are answering different questions. (I was born in the town of Ballinasloe in County Galway, but my mother's place of residence at the time of my birth was the town of Birr in County Offaly.)
That's my memory of it. My British passport is expired, and is probably somewhere in my parents' house. I don't actually know what it says on it. I do clearly remember that at least one British form of ID I had at one time recorded my mother's place of residence rather than my actual birth place. I thought it was the passport. Maybe I was wrong.
My British passport says I was born in Birr; my Irish passport says I was born in Galway. These are both correct, because they are answering different questions. (I was born in the town of Ballinasloe in County Galway, but my mother's place of residence at the time of my birth was the town of Birr in County Offaly.)