In either scenario, from a genealogical (not to mention, legal) point of view, any offspring would technically be considered first cousins, but their DNA would be hard to distinguish from that of full genetic siblings. Furthermore, it would be almost impossible to figure out who the biological parents are based on the DNA alone (of course, that explanation is too tidy. There are also other factors that might make formal identification possible).
How can this be? Think about it for one mind boggling moment...
Identical twins share the exact same genetic material, egg/sperm and all (while fraternal twins are conceived from a different egg and sperm). So in this case, the four "sets" of DNA are the same as only two sets.
To explain further;
Biology... you can't make this s*!& up.