Neither.
To my mind, if there is absolutely no evidence of where a person was born, such as is often the case with children whose parents migrated from one country to another, say from Germany to the USA, where the child could have been born in the country of origin, in a country between Germany and the port of departure, at sea, or after arrival in the US at the port of entry, and there's no record showing where, then it's a bio item. I certainly don't see that a category will be useful for this.
Same principle applies to place of death.
The DD error for this lack of location could be amended so that, after due diligence, when it has been determined that we don't know and never will know where, the location could have Unknown entered into it. Right now Unknown is not allowed in these fields.
There are oodles of profiles that I have seen created long ago that have location boxes blank. The majority of them on research wind up having at least a country / region possible to enter. It's a bio item, or Researh notes item.
I certainly don't think an additional category line will be useful for these.