If I had a double-d handle, I'd use that. But I just use a bar under a barbell, so hands facing body. I don't really think there's much of a difference.
I typically perform T-bars with a 10 inch overhad grip. . .I feel that the underhand grip places immense stress on the biceps therefore I stick with the overhand grip because its safer IMO.
Sometimes I will use a parallel grip. . this places additional stress on the brachialis.
Bottom line is. . find something that is comfortable and works for you.