Two of my grandparents have been afflicted with this illness. I have seen it happen two different ways.
My paternal grandfather recognized his condition first and told my father he could "feel his mind going." All his life he was very physical, and I believe this helped him because he never degraded in this way. To the end he would go on long walks with my grandmother (at the very end he did have some of the bowel problems though). His illness just affected names and specific facts.
My grandfather was a flight engineer in the Army Air Corps during WWII. He flew in a B-29 over the Himalayas and bombed Toyko. However, he could not tell you this and instead would point to a wall of pictures and documents made by my grandmother and say, "Tell them about the thing."
This happened with names too. You could tell by his excitement he knew who you were, but he got the name wrong and instead used the names of his children.
There was some redemption during his last day where he was perfectly normal. My grandmother and him spent the day together like before the disease; walking, talking... laughing again. Then he had a stroke that night and my grandmother decided to let him go. It was a good decision. Ending on a high note
.
Now my maternal great grandmother is a different story. She needs 24/7 care because of the degree of her illness, and because my great grandfather is 90 as of November, 2010. (On a side note he is also a WWII veteran having fought as a sniper in the Army's Deadeyes 96th Infantry Division in the Pacific.) Alzheimer's has affected her in several different ways.
She does not remember the names of recent additions to the family, but she does know all of her great grandchildren once you remind her of the name once. To her our faces are quite a bit younger.
She does not remember where she is because there have been renovations in the recent past to their house. In her mind that wing of her house does not exist. Plus they have a big LCD TV (really big), which makes her think they are at the movies all the time.
As for my great grandmother's physical condition--it was the first thing to go. She has been in a wheelchair since her initial fall and diagnosis of Alzheimer's years ago. Plus she cannot do much of anything by herself. A caretaker feeds, clothes, washes, and watches her 24/7. However, don't think that she has lost everything.
Her memory is fantastic when it comes to old movies, trips, and events. It is almost like she is just living in the past.
I hope this gives you a better outlook on everything. There are obviously a lot more cons than pros because ideally the disease would not exist at all. I'm just saying that from my two experiences the actual person does not completely disappear.