I have both but not compared them the same way yet. With the DirectStream (DS), I have connected via microRendu both with USB and then with Matrix from microRendu and then I2S to preamp. The Lumin X1 takes significant break-in of at least 200 hours but recommendations say double that and I am getting close now. It truly has dramatically improved from the out of the box and as I continue to add plaing hourss.
Lately I have been experimenting with running the X1 straight to active crossover and not using the preamp. I have not tried the DS that way. I will try to cut some time this long weekend to do that and will do listening using the same XLR cabling from the DACs to the active crossover.
I really like my preamp,a Vinnie Rossi L2 Statement DHT, which also has a DAC. However, the X1 direct to active crossover has provided excellent results. If you do not have other sources you wish to use, this makes for a very simple connection system. It will be interesting to do this with the DS. Both PS Audio and Lumin provide free updates to their platforms. I was one of the early ordering owners of the DS, and it has been completely trouble free for me.
I hope to post my impressions next week.