The D18 is all about smoothness, with a subtle warmth to it that really flatters most music and gear. It's hard to assemble a system that the D18 doesn't sound great with. That makes it great fun to listen to but not ideal if you wanted to use it in a home studio or other critical listening scenario.
The Concero is more neutral, more true to the recording for better or worse. It can be very ruthless with poorly mastered tracks, and certainly isn't the DAC to use with a revealing amp and HD800 if you are on the fence about enjoying the HD800 type of sound.
My current favorite combo with the D18 is to pair it with the exceptional sounding A18 matching amp, using XLR, and then add the latest LCD-2 with balanced cable. That combo just oozes musicality and hits about as hard as anything I've ever heard short of a huge reference level subwoofer.
In contrast, I currently prefer pairing my Concero to my Analog Design Labs SET amp, and from there driving a Beyer T1. I didn't initially love this chain at first but it has grown on me with its crazy ability to resolve even the finest micro-details. The mids are just liquid and effortless, and when used to play a reference level recording - watch out.