Sorry for replying to such an old thread, but I almost sold my Kemper and/or Apogee Duet over the same/similar issue that I just resolved and hopefully I can help out someone else in the future. The Kemper headphone output sounded so much better than the Apogee Duet and I made sure that the Space parameter was turned on for both, all EQ was the same, volume was the same, both were using Stereo, etc.
I added a heavy ping pong delay effect to test out the theory that I wasn't hearing in stereo out of the Apogee Duet and lo and behold it was mono, while the Kemper headphone out was stereo. So it turned out that even though I was recording into the Duet in stereo, in the Apogee Maestro software, under the Mixer section, there are knobs to control the input channels and by default, both are panned dead center. You have to pan one channel all the way to the left and the other channel all the way to the right to get a stereo sound.
Sounds obvious looking back, but it's really easy to overlook this setting amongst all the different variables here. Hope that helps anyone else out!