I have on 03' Byerly and that is what I've been riding since, well 03'. Good board with alot of nice features. Pops well, but demands good fundamentals. I ride it with the stock 1.1" fin, but probably should go down in size.
I rode my bro's 04 absolute, and I don't think it's any different from the 05, but I could be wrong there. To me, it seemed a bit harder to make the absolute take off when cutting. I don't know if that necessarily means it's slower, but it just seemed that the Absolute did not initially cut as hard.
The pop is very different. The Absolute had a smoother pop, the Bylerly bucks a bit, but I like that as I am bigger and need every once of upward force I can muster.
The absolute had a smaller center fin and was way looser on the water. The Byerly's glassed in fins are pretty agressive as well.
They may look alot the same, but feel a good deal different on the water. I would buy an absolute in a second and know that I was making a good decision. I stick with my Byerly for now because it does alot of things very well, and it has lot's of skulls on it.