That's a difficult question to speculate about, especially since we don't even know if this sort of copy is possible. But if we assume that our memories are somehow stored in our brains, like they are stored on computer media, and if we think of the mind (or soul) as software, also electrochemically stored on the brain tissue, then, presumably the copy would be identical if it were executing on a comparable brain.

That's a lot of ifs, but it is all based on an interpretation of the mind as a purely physical phenomenon. My own prejudices lead me to believe that, but I have no way of knowing for sure.

However, there are physical limitations to the concepts "identical" and "exact copy". At the quantum level, no two complex objects are totally identical, they differ minutely because the exact state of every particle cannot be predicted (i.e. known) to infinite precision (Uncertainty Principle). The same can be said for the new hardware, mechanical or biological, the software copy is now running on. Whether or not this would be noticeable to anyone else is anyone's guess.

At any rate, the physical mind is an electrochemical phenomenon existing in a constantly changing substrate. It is changing all the time anyway, even without our having to postulate any extraordinary technologies. Any changes brought about by copying would be obscured by the normal changes due to metabolism, etc.