The primary difference is that at lower power (say 100-200 watts) there is still a tiny bit of something that isn't going to be exactly Walkabout (and this differs between individual Walkabout amps too) but as soon as you get above ~200 watts and the Walkabout becomes less controlled and overly bloomy (to some), the WD-800 remains true and solid. This is ESPECIALLY true at 2 ohms, where the Walkabout struggled with articulation (and reliability). It's a necessary trade-off, but with the extra features and control, the end result (IMO) is much more usable then the Walkabout at higher volumes.
I was just answering a PM on this. For those who always used the WA at the ragged edge and loved that phenomenon that was bordering on instability, the WD-800 never did that. I'm mainly a clean player and rarely tread into that kind of territory unless it's a signature sound for song, so I never liked that regime on the WA. The more I thought about it, it sort of made sense to me that if I got all that sweet WA tone and could have it most any volume I wanted, the trade off was that I would't be constantly running into total break-up.
In my time with the prototype I really liked that I got usable WA mojo (the rich tone and harmonics) at really high volume and the head stayed focused and composed. That's not to say you can't get a little grit if you want it, but this new head (thankfully for many of us) didn't seem to have an operational state where it was the sonic mess the WA could become.
As I looked over my test notes Chef and I both mentioned that one aspect during our time with the prototype, and were of like mind that the WA goodness that you could have at significantly higher power levels felt like a good trade or compromise. Additionally, with the better control tapers and extra tone shaping tools (specifically the HPF and damping control) you could dial in and fine tune the voicing in more ways than the original WA.
My sense is that a lot of WD-800 magic happens by deliberate design in the pre-amp voicing and familiar controls (even the mid control circuit behavior felt literally identical to the original) and user selectable damping control. In contrast, in the original WA a lot of the tone seemed to be more a tolerance stack-up luck of the draw interaction between the pre and power amp sections that could be all over the map based on volume. Please remember that I love the original WA and still own two of them, but I'm honest about its oddities and shortcomings.
IMO the WD-800 kept the best of the original WA tone and added more voicing control that once applied will remain consistent as the volume goes up to whatever level you need, while remaining stable in 2 Ohm operation.