Based on the grandparent's logic (which I support), they would both be equally "you", assuming it was a perfect duplicate. From that point forward, the two people would have different experiences, and so would become different people, just as you have different life experience now than you did a week or a year ago, and so think and behave somewhat differently.
That said, I bet they would also have a pretty fascinating relationship: like a twins bond, except much more so. Given their shared brain structure and largely shared life experience (shared to a degree that no two separate people could), their thought patterns would obviously remain very similar. It would probably feel very much like they could read each other's minds.
That said, I bet they would also have a pretty fascinating relationship: like a twins bond, except much more so. Given their shared brain structure and largely shared life experience (shared to a degree that no two separate people could), their thought patterns would obviously remain very similar. It would probably feel very much like they could read each other's minds.