Spoke to Bruce at great lengths about this. So... Apologies in advance, @mentoneman
Bruce and Avi (owner of BAD) are very close friends and get along well. Bruce had always had a partnership with Avi even before BAD was a thing - back when they were called ETI and Bruce was doing amp designs for the B52 line. If I recall, ETI and that whole business actually started as cabinet makers for like car speakers or professional audio enclosures or something. ETI first tried to jump into the line of amps to sell to Guitar Center, and they reached out to Dave Friedman for help because their very first iteration was apparently pretty bad. Dave pawned it off on Bruce, and that's how Bruce got involved with them originally.
Fast forward a bit, Bruce eventually sold the rights and everything regarding his Egnater name to ETI which became BAD. Main reason for selling it was because it allowed Bruce to focus on the design part - the part he loved the most, and Avi could focus on the business part which Bruce always hated. The plan was to use Chinese factories to make everything and keep the costs down, but have Bruce design the circuits so they're good sounding amplifiers. They'd then mass market them at Guitar Center and elsewhere at extremely aggressive pricing, often becoming people's first tube amps. Because they had access to all these Chinese manufacturing facilities, they could literally make pretty much any part from scratch.
Tangent story time... Egnater Rebel. So that amp originally just had a lever to switch between two tube types. You could swap between 6V6s and EL84s. At the very last minute, BAD's legal team identified a patent issue where, I believe it was Mesa had a patent on the switch to select between two different tube types, and they were in danger of possibly being sued. Entire production line for this new amp halted because of it. Avi phoned up Bruce while he was on vacation and basically made him design something to put in that same place on the spot. Bruce came up with this crazy 4 gang center tapped potentiometer to blend the amount of each tube instead of simply switching between them. The Chinese facilities custom made the pot for them on the spot, and they were able to save the production line, coming up with a totally new way of handling mixing tube types never seen before. Pretty sure this was patented.
Anyway, the amps were great and everything went well. However, they started noticing some strange failures in the field regarding transformers. Bruce said that's impossible, the transformers were spec'd perfectly fine. They started taking them apart and investigating. They found out the Chinese suppliers were cutting corners. So they flew over to China and told all of the facilities to stop cutting corners, they need to be designed exactly as specified. It didn't matter. Even if those facilities stopped doing it, the facilities they got their supplies from were cutting corners that preventing them from meeting the correct spec, and that one aspect alone basically ruined his entire name. They eventually got reliable replacements towards the end, but the damage was already done, and the Egnater name was no longer really "cool" anymore. The lack of perceived reliability kinda was the nail in the coffin.
None of it was Bruce's fault, but it was definitely a lesson learned...
To get back to your question - Bruce really only has a few handful of designs. They're all twists on his original IE4 circuits, his Megadrive circuit he did for Marshalls, his Boutikit... CH3 is the classic Marshall-style circuit. CH4 is the added gainstage and making it nice and warm, but still keeping it tight. He was the main guy who popularized the tight switch, after all. So you are indeed correct, they have a certain "Egnater" character because he tends to shape their sound that way.
The most different sounding Egnater circuit is probably the Vengeance / Armageddon circuit where they tried to cater to the metal crowd. The Armageddon has the ISP decimator since he's friends with the Rocktron guys, and he also has this mid circuit in it which he got from Peter Diezel (with Peter's blessing). There's a fun story about the Armageddon and djent guys, but I'll save that for another day.
If anyone ever gets a chance, go take his amp building class. He's going to retire soon, and there are very few slots left. He loves to chat and tell stories, teach people about amps and amp design. And he's probably had his hands in way more things than you'd ever imagine... Lots of things that have other people's names on them are actually his design since he does contract work for a majority of companies. Everyone at BAD, Fender, Bad Cat, B-52, Randall, Rocktron...
