The closest things I've heard to Jazz are songs by Frank Sinatra, Billy Paul, and hip-hop jazz. So far to me, everything I've heard from it has it's own atmosphere, and some recordings will sound bigger than others.
Based on that, I would recommend the H3 to you, and if you can afford it (Heck, you have amps and everything) you should go for it.
I can't compare these to the Dunu 1000. The best I could do for you is listen to some songs you recommend and try to communicate what I'm hearing.