The short answer is that the Ego DACs use USB power (it's all they have) - but that power is stepped up, converted to a split supply, and then filtered and regulated.
This means that a little noise on the supply line isn't usually a problem.
On the DC-1 and the XMC-1 the circuitry is all powered from the unit's AC power supply.
However, there's also a context when you talk about noise......
For example, the power supply in the Ego DACs is seriously filtered and regulated, so noise on the +5V supply probably won't get through.
And, if you're listening with headphones, noise on the ground won't matter (because headphones have their own "floating ground reference".
However, if you use an Ego to connect your computer to your stereo, and there is noise BETWEEN their two grounds, then a tiny bit of that noise might sneak through.
So, depending on your computer and your stereo, you might find that the Ego picks up some noise....
However, in that exact same situation, the DC-1 probably won't pick up any noise.