keyboard101
Sorry to be so long getting back to you on this, but I have been retracing my steps on the web to things I had read and seen over the past couple of months that are related to this topic.
My first impression was - how could you like the sound of the XP so much and dislike the Di so much, when they are basically the same sound engine, but I did not want to say that openly without being certain.
The first link below is to a reply posted by artemiy, the moderator over on the Roland Clan Forum, where he states that the voice architecture of the Juno-D is that of the earlier Roland RS series while that of the Juno-G is that of the Fantom-X. The Fantom-X specs on the Roland-US site show that it accepts the SRX expansion boards, which places the Fantom-X, and consequently the Juno-G, firmly in the JV/XP "sound family". In the second link below, note the point where Luke Edwards of Nevada Music (the demonstrator) answers the Sonic State interviewer that the Juno-Di is considered an upgrade over the Juno-D, as it now uses the sound engine of the Juno-G, so that now places the Juno-Di firmly in the JV/XP "sound family". My whole point to all of this is that if you can get what you considered good sounds out of the XP, you should be able to do the same with the Di. That is also my point with both of the YouTube links - if those guys can get that kind of sound out of the Di, you should be able to as well.
You need to consider that you are comparing the Di, an entry level synth, to the 61 key version of the 76 key flagship XP-80. A major part of the "difference" could be in the quality of the "sound support" circuits - mostly the internal pre-amps and final amps. So, where the XP's did pretty well right out of the box, the Di could probably use a little help. That is, it could probably use a little tweaking. I am sure the units used in the "official" demo videos have been highly tweaked. You might want to take a look at the sound enhancements starting on Page 94 of the manual, but those are on a sound-by-sound basis. It would probably be better to start by looking at the EQ of your current external sound system and tweak it to match the new Di. If you have not already done so, it would also probably be a good idea to download and start learning to use the Juno-Di Editor.
http://forums.rolandclan.com/viewtopic.php?t=28782#p176023
As an added note, you might also be interested in this thread over on the Roland Clan Forum, where they are currently discussing using the Juno-Di Editor to manually port JV/XP patches to the Juno-Di (Also further evidence that the Di is now in the JV/XP "sound family").
http://forums.rolandclan.com/viewtopic.php?f=35&t=47329
Best of luck !