I play mostly in Eb and drop C# with my les paul custom-based Short Hydra with the holy diver in the bridge position and my heavily modded 50w 1973 Marshall JMP
the amp had an original Lee Jackson mod/rebuild, but I've done a lot of changes throughout the years (the original mod was way too dark, bassy and farty), so right now it has some sort of plexi/diezel vh4 hybrid circuit
this combo sounds great for most of the stuff you mentioned
I use a tc classic sustain parametric eq as a compressor and output/midrange booster, though, but my amp has a lot less saturation than an actual diezel vh4 on ch3 (I'd say it's around a non-boosted bogner shiva max gain level)
the black dog might have better picking articulation under gain, but the diver sustains better
I like the dog better for Gilbert-like medium/low gain leads, and maybe for Soundgarden stuff