The slimx copes better with many MP3 formats - but once again, if absolute sound quality is the issue, you wouldn't be using MP3's - of course you will! With a good-source MP3 (320K CBR for example), the D-CJ01 sounds very good indeed. Both players have the slightly annoying pause between tracks when playing MP3's.
With CD, there is no issue with either player. With the SlimX I had, I got a track delay but I understand they've fixed that with new firmware. You know, the firmware feature is nice but it seems that they're fixing bugs with each release more than anything else - in comparison the D-CJ01 stands relatively bug free.
The D-CJ01 works out more expensive in the end, because you'll want the RM-MC11EL remote. Europe-spec models ship with this remote, which is the reason that they're about $50 equivalent more expensive.
The reason I made my choice is that close up, the SlimX just didn't look as nice as the D-CJ01 and it didn't sound quite as good (although it was louder). Folder navigation is easy on the D-CJ01 (there are a couple of dedicated buttons on the unit, it's slightly more convoluted on the remote but not unduly so), I don't use the radio, I don't have a need for equalization features.
Finally I liked the SlimX remote for the sheer amount of info it presented, but it was a bit geeky for me - and I own a number of RM-MC11 remotes now
so a spare was nice.