I want to chime in here as I have had experience with both. I first had the DAC1 - I was running this connected via digital coax to an Empirical Audio Freeway. I used it both in SE mode, and then when I got balanced cables for the HD650, in balanced mode straight out of its XLR jacks.
It was excellent, no doubt about it. Clarity and speed were great, as was instrument separation and positioning. I tried it with a few other headphones too, and with each (HD650 included) I ended up finding it a little too sterile. It lacked an element of body and warmth. This was particularly prevalent when running the DAC1 to the Stax SRM-717 and Omega II.
I then got the Apogee Mini-Dac USB. At first I used it via USB, but after moving my computer source from PC to Mac, I run it straight from the Mac Mini's optical digital out via a Van Den Hul Optocoupler cable. This allows me to use it at 24/96 (USB limited to 24/48 on the Apogee). The headphone amp in the Mini-Dac is very competent, if a little warm. The balanced output worked a treat, especially with the Stax. I also used its XLR outputs for the HD650 in balanced mode.
I have read on occassion when people compare these two DACs that they say the DAC1 is more detailed. I think differently - I found them to have the same level of detail extraction, as well as articulation. The DAC1 has the edge in speed, but I prefer the warmth which the Apogee brings to the party. It is not as clinical, but certainly not less detailed. When I listened via the Stax, and with my newly acquired balanced SA5000, it was evident that detail is one thing this DAC does not lack. Perhaps the speed, and cooler nature of the DAC1 (can call it "neutrality") is what some people have reported as more detailed.
I am personally thrilled with the Mini-Dac. I cannot imagine what the SA5000 would be like through the DAC1, but can only assume it would be similar to the Stax experience - great at first glance, but fatigue very soon sets in.
Cheers,
X