I think Rev_Slinky hit a lot of key aspects.
I will add that the power amp damping factor on the TT is the same on both the Boogie and SW channels (it's the same power amp section). This places the SW channel in the medium to low range...the D-800 has a higher damping factor and feels a little tighter and more SS quick (but not at all sterile). So between the TT's tube preamp voicing and that lower damping factor the SW channel on the TT has some foundational differences to the D-800.
I would also add that the TT's SW channel benefits from access to both a deep and bright switch (very usable), user selectable gain (drive level) for the tube preamp, a variable HPF, a semi-parametric mid EQ, and user adjustable OD symmetry. Depending on your playing style there is a lot there to get you some versatility the D-800 is hard pressed to match. Also, as mentioned the TT overall (both channels) are a fair bit inherently brighter than the D-800 right off the bat (although not in your face or annoyingly bright).
The D-800 sounds very good and offers the voicing control (a very useful feature) as well as two nicely placed mid EQ adjustments. While it does have an HPF it is not user adjustable. The D-800 does sound inherently warmer and to me feels a bit quicker/faster (which I attribute that to damping factor differences and it is mainly at lower frequencies where you would notice).
It would be easier for me to get a TT to sound close the D-800 than it would for the D-800 to get all the voicing and feel variations I can get out of the TT's SW channel. I own both but if I were forced to choose, I would keep the TT. That said, I don't feel in any way disappointed or relegated to a second rate amp when I use the D-800. The TT is essentially two exceptional amps in one box and as versatile as the D-800 voicing control is, the TT offers more options for me to adjust directly.
I hope that's useful....it's a data point from someone who has a lot of time on both heads but may hear things differently from you.