Is the flatness of DC output of a typical ATX power supply unit worse than a power adapter?
The ATX power supply is a switching power supply. It's important to be sure of the difference - a switching power supply switches the voltage at a much higher frequency (e.g. 65kHz) so smaller transformers can be used (transformers work more easily at higher frequencies) 
The downside is high current switching can easily cause EMI problems if not dealt with properly, and often in cheap power supplies (e.g. ATX) the filtering is very basic and may not always meet regulations.

A "standard" supply uses the 50Hz or 60Hz mains frequency to change the voltage, so the transformer for the same amount of power would be much larger. The supply size will likely be over twice as big for the same rated output. However with low frequency and (usually) linear regulation, these supplies are usually quieter. Are you absolutely sure your "AC/DC" supply is a switching supply? 

It is relatively easy to make a quiet supply using either design though, so you may find a well made SMPS (can include linear regulation after initial switch regulation)  is quieter than a cheap (possibly unregulated) standard supply. 

I think your noise may well be present all the time, and causing issues with the sensitive (active I assume :-) ) analogue speaker circuitry. It may be (as mentioned previously by Madmanguruman) from the PC/monitor plugged causing problems with regulation, or could be a grounding problem of some sort. Depending on the frequency (be good to know roughly how high/low it is) it would be easier to guess at what is causing it. An scope on the lines would tell the full story.