They are essentially clones of each other and much can be learned of the reductionist aspects of consciousness from such twins. I have been fortunate that two of my acquaintances were identical twins. I could not tell them apart except from talking to them.
Despite almost identical nuturing as well, same clothes, etc., they were different mentally from the beginning, according to their parents. They were certainly different for me. For example, one was a consistently faster runner than the other. It seemed that it was simply because one wanted to be the faster runner and the other did not care. I have always considered this evidence for reincarnation of different souls in identical bodies.
It goes without saying that they had separate and different consciousnesses. They also had different interests and motivations. Even their emotionality appeared to be different, one being much more sensitive than the other.
Of course as they grew up they became less and less exact clones of each other. But still identical twin studies are perhaps the best evidence of just how reductionistic consciousness is.
For example, are memories electronic in nature. If so, then an exact duplicate on earth and mars should have the same memories, and in that sense be the same person until new, different experiences become different memories in either person. Unfortunately, identical twins do not provide evidence of the nature of memory.
On this forum I am of the extreme non-reductionist view, believing that memories are at least mostly non-electronic in nature. I further believe that such memories can travel outside the body. So if the memories of the mars person were to travel to the earth clone, then the earth person would become the actual mars person transported to earth, and the body left behind would have anesthesia.
It follows that resurrection must include memory resurrection as well as body resurrection. On this subject I have to respond to what Dennett calls the work of scientists versus the intuition of ordinary people.
Dennett presents a myopic view of what scientists think, suggesting that they all think exactly like him. Just read the on-line moderated forum, 'Quantum-Mind Digest' to realize that scientists are much more imaginative than ordinary people, and have proposed an entire spectrum of theories from reductionist to the non-material to explain consciousness. Much of the thinking of scientists on consciousness is based on their own intuition. Dennett knows this well and should be chastined for invoking the 'what scientists think' argument.