Audio-only capture on AES with sample rate conversion off will take the audio clock from the AES input.
Audio-only capture on AES with sample rate conversion ON, or analog capture, will re-clock the audio to video reference (which may be internal to the DX if you don't have a master clock). (The input AES stream is always decoded from its own clock.)
A/V capture on AES with sample rate conversion ON, or analog capture, will re-clock the audio to the active video input. With SRC off, it still uses the AES input for audio clock, and assumes it's externally locked to the same source as video in.
DX is a two-clock system and will usually output the E-E on reference. When doing the clock correction for E-E output on reference, it uses a simple converter that is not considered broadcast quality to create the monitoring output. I can't hear the difference, but if you are sensitive to it you might hear that. The captured data is before the conversion, and is pristine.
However, under some conditions, Nitris DX will also clock the output audio on the input clock, and in those cases you must be careful not to cable up a clocking loop. That is what gets most people into trouble - when the deck is referencing its inputs.
For the most people, if you just want to bring in the audio, just hook the deck output to the DX input and press record in the capture tool, you'll be fine. If you also hook the deck input the the DX output, you're in danger of wiring up a clocking loop, where each piece of equipment tries to clock to the other, and they wander off into the weeds.
Do you need time code accurate capture? That gets more complicated, because deck control wants to know when the video frame edges occur, so it can send commands the correct time. It has been too long since I did that, so I don't remember all the details, but it can be done. It requires the DX and the deck have external reference.
If you need more sophisticated control over clocking, there is a bit in the "audioextras" console command that will give you manual control. This is sometimes needed to override the use of video in clocking when you know everything is synched to the same external master clock. This is often needed when using an digital mixing board that connects to both the DX inputs and outputs.