I would say build quality is close but playability is different. A lot of the design attributes and the ergonomics from Jackson are present with Caparison @ThePIGI King.My TAT II is one of the best playing guitars I own. It feels, sounds, and plays incredible. It is right behind my ESP MII-UC. I only have 7 string J Customs and don't have any experience with 6 string J Customs but I'd say that they're pretty on par as far as I can tell from playability and sound, at least for me but I have never really had much trouble or problems with any guitar; I'm not too picky as long as it is an Ibanez RG570 with 18 V EMGs.
I was also going to post but then forgot in response to another comment made earlier in this thread that I doubt the company cares much about increasing production. They seem to be content and proud of what they do at the scale that they do: https://www.caparisonguitars.com/about/
For context, some history of why that is although much more info can be dug up on forums over the years: https://en.wikipedia.org/wiki/Caparison_Guitars