After several days of listening, I thought I'd come back and flesh out my observations. Compared to the DAC2, the DAC3 allows you to listen into complex arrangements more easily. On recording that allow it, the soundstage seems bigger and deeper. It is also easier to hear and appreciate the texture of vocals and instruments - I'm especially enjoying listening to the deep growl that both acoustic and electric bass can make, and the variety of tone achieved by different sax players. I spent quite a bit of time making sure I had levels matched, and the differences I hear held up to that.
When trying to write about them, it's easy to exaggerate the differences between DACs - they're not like the difference between speakers, rooms, or recordings. In the grand scheme of things, the improvement I hear isn't huge, but it's important and worthwhile to me. This is not going back at the end of the 30-day trial period.