My impression is (으)나 is closer to "Never mind that/whether [...]"
우리는 차가 있으나 택시를 타고 간다
Never mind that we have a car, we get a cab
우리는 차가 있는데 택시를 타고 간다
We have a car even so we get a cab
=> Although we have a car we get a cab
Could someone help to clarify this?