Here's a little history on diamond for ya so things will be cleared up. Diamond audio purchased out esoterric audio a long time ago. Esoterric used to be a super high end car audio company. Diamond re-bagded the esoterric amps as d7 amps.
The d7 is a VERY finicky amp (i know this cuase i used to have the d7054). I have compared it side by side with the d5600.4 and i would have to say that the d7 does sound warmer then the d5. but that's really just a personal thing.
The d6 is a revised d5 amp. The d6 has a much MUCH better power supply. Cleaner, more stable, and more power (even though they are rated the same. BUT i REALLY do like the looks of the d5 much bettter then the d6 amps.