That is both amazing and scary at the same time. What happens when(if) we manage to simulate a larger mind, and a larger one, up to human level. What happens if we get a computer that can simulate hundreds of minds and construct them in a way that they work in a group to solve problems? We can capture hundreds of years of evolutionary problem solving without the need to program all of it from scratch. More importantly, what does that mean ethically? Do these simulated minds count as humans? What if we do not simulate their ability to feel pain or suffering? Does a computer count as the person, or does the simulated space count as the person? Does turning off the computer count as murder? I get the feeling that should these projects get to higher scales, these are going to be the next generations, or the next-next-next generation's abortion issue.
My assumption is that currently, you are the arrangement of particles and matter in your mind. If you create a second copy of you, that is not you, it is a copy. It isn't made of the same matter, and both machines can exist at the same time. The only way to really "transition" is to do the same thing that we do in real life as our minds develop. Slowly replace and reduce the cells in the mind with artificial ones, and have a slow transition that lasts over years. That way there can never be a "copy" of you, and "you" are defined as the half-half being during the transition period.
These are good problems to have and good questions to ask. It means we are advancing...to the future!