My experience has been similar. The output on my MacBook was fine, until I hooked up an amp (coincidentally, my headphones are also Beyerdynamic; DT880s in this case). It sounded pretty bad to be honest, so then I hooked up the external DAC, and it was fascinating how big a difference it made. And I'm not an audiophile, so I usually don't really notice such differences.
So my post is downvoted to -3 and then bumped back up to 0. But there was no disagreement in the form of a response.
I'm not an audiophile either, but there is something about having listened to a track over and over again on an average pair of headphones and then listening to it again through a DAC and the DT770s I have. It's like hearing it for the first time again. Details just pop out and I really began to appreciate the engineering that went into some of the 80's songs I listened to on crappy car speakers when I was a kid.
BTW, the tracks I used to test the spatial qualities of my macbook was "Hard Time Killing Floor Blues" on the O' Brother Where Art Thou soundtrack, and "Blackbird" by the Kings Singers.
With the DT770's alone using the Mac jack, the Mac smeared the audio on both tracks. The first one especially because the mic used for recording introduces a distortion.
With the DAC, spatial on both were clear and came from point sources. Phenomenal.
* the DAC and AMP were Schiit Magni/Modi