As Australian, I'm going to have to be Devil's Advocate for both parties.
Firstly, Random House Dictionary has this to say on the matter:
Cookie:
-noun
1.
a small cake made from stiff, sweet dough rolled and sliced or dropped by spoonfuls on a large, flat pan (cookie sheet) and baked.
Biscuit:
1.
a kind of bread in small, soft cakes, raised with baking powder or soda, or sometimes with yeast.
2.
a.
a dry and crisp or hard bread in thin, flat cakes, made without yeast or other raising agent; a cracker.
b.
a cookie. <-- ?
So thus far, it seems the American cookie can be a British biscuit, but not necessarily vice versa. It does seem to be talking about methods of creation, though it's probable (by the pattern in oreo) that it is simply poured into a mould. I won't deliver a verdict, as I'm simply supplying fuel for the fire.
Secondly, wikipedia had this to say:
So can we just please agree that an oreo is a "sandwich cookie", as a variation of what is known as a cookie / biscuit and all get on with our lives?
Peace, children.