xP I don't really believe in reincarnation, but if I did, I thought it might be something like this: ^.^;
You have your "soul" and you have your "spirit". Your soul is just something which keeps all of your lives, and your spirit is, well.... You, in every life. And in each life, when you're born, a new spirit is created. You might occasionally have memories of past lives because part of your soul is in your spirit with you.
Your soul is, basically, your life essence.... And your spirit, basically, branches off of that. ^.^; Whenever you are reborn, a new spirit is created, but it's still "you". You'd have a completely different daemon and everything, but you're still you.
Even if the daemon
did stay the same, you would stay the same, too! And your past life memories would be locked up inside you. Plus, the daemon can access your memories and all that easier, and since it's also a little bit of your subconscious, knows what's right for YOU. So, really, the daemon is not older than you or anything, because it would stay exactly the same, and so would you. ^.^; You just wouldn't have quite the same knowledge of your past life memories as it would. XD
And for past life memories? Well, some people might have more of that "soul essence" than others. They might have more of a soul essence if they still had some lessons they had to learn in their past life, and by learning the lessons in your current life, your past lives will be completed. Some people, such as Otherkin, will have more of that "soul essence" than others, that stays with them all throughout all of their lives. Some other people, however, will have next to nothing of that "soul essence", because they learned everything they needed to know in their past lives.
.... I fail at explaining things. XD But even though I don't believe in spiritual things (MY THEORY, HOWEVER, IS TOTALLY PLAUSIBLE & U NO IT >:D), I still like giving a lot of thought to things I don't believe in anyway. ^.^;
I just haven't come up with a scientific explanation yet. XD
Here's, like, a picture:

Even though I didn't include the "soul essence" in that one. Oh, well. XD The person portrayed in this would have no past life memories at all, then, 'kay?! O.o;
I think once I had a tiny flash of that I was a princess or something in the Medieval times. ^.^; But I was watching a castle or something burn down. And it was just a little split-second flash. D:< NOT FUN TO WATCH!