I own both Emeralds and Black Dogs and have one in an Epi LP and another in a Edwards.
The Emeralds are much hotter beasts than the Black Dogs, like Jonathan said, the Emerald has also a tighter low end, which makes sense, as it otherwise could lose definition with too much oomph and high gain.
Depends on what you go for. I like the Emeralds for being hot and crunchy on rhythm work (think GnR type of Marshally tones) but stay thick on the high notes in solo work. The Black Dogs are just great for all kinds of styles, but excel in mid gain applications - they are more organic sounding than the Emeralds.
Abraxas I don't have any experience.