andaruGO somewhat plays with this "improvisation style" that jazz is famous for, actually. He writes everything in live mode and plays the gameboy by itself, mostly, in all his shows. Ive seen several people do this so he's not the pioneer. However, he uses the pause function as a means to create a beat skip between tones which i find pretty good. Jazz is, though, one of the hardest things to mimic, i agree.
I very rarely post here but I was directed to this thread by a friend 
Personally, I believe that due to its robust nature and the sound quality-- the DMG is fantastic for all applications. However that is not to say that it is the 'end all be all' by any means. Whichever gameboy you want to use in your live set or recording is up to you, but from my personal experiences of playing live and recording have shown me 'the light' so to speak-- as far as button placement, sound quality, 'modability' and cost, I truly do believe that the DMG is a superior machine.
I have huge hands, and the DMG fits perfectly into them. I also enjoy how easy it is to get the thing open (as well as how easy it is to SLAP new shit into it).
I would definitely like to address what Dotmatrix said--
I use LSDJ programmed in 'live mode' with patterns slugged to loop infinitely unless I press start on another loop.
(so on the song screen it would look like)
pu1 pu2 wav noi
00 03 06 09
-- -- -- --
01 04 07 0A
-- -- -- --
02 05 08 0B
the '--' represents an empty space, so in the theory of how LSDJ plays through chains it would loop indefinitely unless acted upon by me pressing (or double pressing) start on a new chain. I truly think this is a great way to play songs live, as you are actually playing the song. Additionally, select+b and start+b while having the cursor hover over a chain will solo or mute that channel, so using that on top of the concepts that I laid out before allow for a lot of improvisation. I always strive to use 1xLSDJ because I really like the boundaries that the format and program present to the artist/driver/musician.
There are so many different ways to compose and perform that ruling any one thing out, but that is how I prefer to perform all of my shows (I also use this format to record final cuts for albums etc).
thanks for the shout out though buddy
DMG 4 LYF3 hahaha //// /////////