I've only had the Antiquity JB and the standard JB. And yeah, the Distortion. And the Black Winter if you want to count those.
The Antiquity is hands down the best JB I've had. Not gonna say it was in a completely different league, but it definitely has something special going on. The high and the low end are rolled off, and it has a certain "refinement" to the attack. Feels "squishier" but and a bit softer, but not in a bad way. Not in an A2 kinda way. Even if the low-end is less extended, the pickup overall feels a bit fuller because it has a bit less emphasis up top. A thing that I found interesting is, even if the magnet is degaussed, the output of the pickup doesn't take a huge hit. I didn't find the output to be all that different from the production JB.
Outside of Seymour Duncan, other JB-inspired pickups I've had are the DiMarzio AT-1, the Suhr SSH+ and Aldrich, the Fishman Fluence Classic. And I'm going to include the DiMarzio Dominion in that list as well, because even if it's not all that directly JB-inspired, it definitely has a JB vibe to my ears, loosely speaking, and the specs don't seem as off as well.
Take this comparison I made as a grain of salt. These pickups are not in the same guitar, and one of them is running on a 1M pot, even. But it may get you a rough idea of how close (or different) they are.