The question you are asking is some serious navel gazing IMHO

. It's sort of like asking, why do I like a specific color. Why we like or dislike the SVT and/or 810 tends to be more subjective. I personally can't stand playing through the 810, even though I do agree it's a significant part of the sound. However, IMHO objectively the SVT and 810 are both fabulous designs...it's just not really "my" sound.
The SVT has some subjectively nice qualities. Overall it was originally designed as a high powered and essentially HiFi amp. Keep in mind the amp came out in 1969. The frequency response can be dialed in fairly close to flat, but there is a very gentle and wide band hump centered at about 400hz. I think this hump is part of the SVT sound, and something I call a low mid push. I also hear a certain grindy quality in the mids when and SVT is pushed a little bit. Selecting the 800hz mid control with a bit of mid boost seems to really bring this quality out.
Many SVT inspired pedals seem to produce a tone that is similar to engaging the Deep switch and cranking the amp way beyond it's 300W power rating. Not a sound I would tend to use. If you don't know, engaging the Deep switch actually creates a huge/deep mid cut. IMHO this notch is way to extreme for my taste.