Derek, I went from riding a LF 128 (trip) to the 2005 Demented 131 and the difference I noticed between the two boards was that my Demented was a lot faster, gave me more pop off the wake (you'll go big) and it is also loose on the surface for surface tricks. I don't think there is that much of a difference from the 2004 model to the 2005 model, but I'm sure you could look it up online. As far as the Byerly goes I've never ridden one, so I can't help you there on a comparison between the two.
You should try to see if a local shop would let you demo one. It's a great board!