I've got both and yeah, the DN-D2000J is brighter and leaner than the IE 800 (pity you lost it...). Especially the DUNU's middle treble is more present, "hotter" (no real problem for me, both the IE 800 and DN-2000J are not too bright for my very personal tastes, but the DN-2000J is definitely brighter).
You may also look on Innerfidelity, the graphs also prove that the DUNU is the brighter out of the two.
Out of my simple measurement rig (Vibro Veritas, no professional gear but good for comparisons), it is also visible that the DUNU is brighter and has got more (especially middle) treble than the Senn.