ok, I've had the DP-24 (original with midi and cd) for 5 years, and I bought a Model 24 back in January. I can definitely hear a difference, but it just might be me.
To me the Model 24 sounds more warm and full and like it has a more 3 dimension sound to it.
I don't know if it is because of the analog mixer preamps and compressor, or if its just in my head.
I find myself using the Model 24 much more then I ever used the DP-24 because it's so easy to just start recording with all the controls and knobs right there.
I've used DAW's since they came out way back in the mid 90's and I was just tired of always using a computer, so I got the DP 24 to get away from computers but I found there was still a lot of menu diving so I didn't use it much, The model 24 is exactly what I wanted , everything is right there to reach out and grab to adjust.
I started out many years ago on Tascam 4 track cassette recorders and it feels good to get back to hardware you can touch, but still connect to a DAW if you want to.
But to answer your question, I think it sounds better then the DP-24, I always thought the DP-24 sounded kind of sterile