Hi. I have been shortly diving with JJ (cca 30h). Good unit, very simple and reliable. But also little bit bulky, heavy. Cleaning CL was pain. Next week I am starting Air Dulient Deco on Liberty Heavy with FM CL in 2x3L config. Actually have both units at home right now. (JJ is for sale).
Having both units at home I see the differenct. JJ is very simple "hammer". It does the job. Like they say 4x4 of Rebreathers. Libery has many features, which some may not like.
I decided to try Libery because of the bits and peaces, which some people dont like about it, modularity, its lighter and easier to clean CL. Dry dive was also good. My personal opinion is, that Libery is little bit softer on the volume of CL. With JJ you eather have volume or you dont and ADV shoots. With Libery I knew with every single breath and change depth, how much volume I have left. (hard to explain). Also WOB was better. Didnt like Divesfot HUD, but that may change.
If you are interested in Liberty, I advice you to check
Club of elite divers - LEVEL 3
let me know, if you have some question