I've never had an SVT, so I can't say if the warmth, grit, and drive it offers are "SVT-like", but I know that I ABSOLUTELY love what the TH offers. It gives me the rock punch that I want, while also cleaning up well when necessary.
It's small, light, and has simple controls. The drive and gain work a little differently than you would expect, but once you get the hang of it you can get right to a number of different tones REALLY quickly. The Tone Hammer is the "tubiest" non-tube head I've ever played. I've played many tube heads that WEREN'T as warm and "tubey" as the Tone Hammer.
I will say that it seems to be a polarizing amp... some folks instantly bond with it and love it, while others never get a sound they like out of it. I can understand that, because if you simply treat the drive and gain controls like any other amp, you will not get the response you are wanting based on the position of the knobs.
It's almost as if the Gain should be named "Flavor" and then the Drive should be the "Flavor Maximizer" or something. The Gain is not really the preamp level. You can run the amp stupid loud with the Gain at zero. It has some EQ curve as well as harmonic content enhancement that changes throughout the range, and then the Drive essentially adds dirt according to the placement of the gain knob.
My favorite spot for rock with a hot P bass is both gain and drive at about noon. Just a lil EQ to taste: +1-2 bass, +2-3 low mids, - 1-2 highs. So yummy!