That isn't materially different than what currently exists, which is basically that your memories last your lifetime, you "die" and essentially become conscious as something else in the same way that you found yourself in your current body.
It's different because dying is fearsome and possibly agonizingly painful. Even in the absence of these problems, a change from your current body into some other form (such that your consciousness and memories continue) is extremely disruptive. Not to mention that you lose contact with those who haven't passed through that change, even if temporarily.
It is categorically different. If your memories of 1000 years ago gradually fade away, only that old version of you is "gone" (in present experiential sense). You and your family and friends have known you as a consistent "self" with mental continuity throughout your whole lifetime. When you die in the current times, you and your family grieve and experience suffering as a result of the lack of your mental continuity. When parts of you later end up in a tree or squirrel, that is not a particularly consoling idea to those who would prefer you continued to exist as a human.