OK, here goes:
Dirac Research's RCS is a software application that runs on a mac or PC and includes tools for room analysis and room correction based one or more analyses. The software is available in two versions, 2-channel and multi-channel (up to 8, as I recall). A calibration microphone is required to measure the room. Dirac offers a mic as an option, but in my testing a better (not necessarily more expensive) mic made a noticeable difference.
DSPeaker Anti-mode 2.0 is an "appliance" and does not require the use of a mac or PC. Actually, the unit is a USB DAC w/ active room correction. The user interface is via a small (but adequate) LCD panel on the appliance. DSPeaker does include a calibration microphone with the device, but IMO the attached cord is too short for meaningful measurements of all but the smallest rooms.
While both units pretty much do the same thing, measure your room and actively correct the playback, there are some significant differences between these products, based on design. Dirac requires a computer and (in it's current iteration) does not support analog input from the source. So while the product is great for playback of digital music files, there is no practical way to use it for analog sources. The DSPeaker appliance includes both analog and digital inputs, and although you can only use one at a time per profile this is a minor inconvenience.
Both units perform well and are easy to use, and will provide correct for all but the most egregious room problems and provide a greatly enhanced listening experience. I think that most users would be happy with either unit. The DSPeaker unit has an obvious advantage for vinyl affectionados (more about that below). But to my ears and in the opinion of my listening companions the Dirac product provides a somewhat better overall room correction experience, for the following reasons:
1- The DSPeaker includes a DAC, and I tested it this way because I believe that this is how most users will use the product. The Dirac application on a mac used an external DAC, in my case an Antelope Audio Zodiac Gold. DSPeaker's DAC was just not equal to the Zodiac Gold, as expected. But when we also tested Dirac with a Meridian Explorer DAC I still preferred the Dirac presentation to the DSPeaker. It wasn't a night and day difference, but it was noticeable.
2- DSPeaker currently supports hi-res (24/96kHz) input via S/PDIF (Toslink) only. USB input is limited to 16/44.1. I routinely play 192kHz files from my mac through Dirac RCS.
3- In the three rooms I tested (small, medium and large) Dirac provided a better overall room correction experience; at least to my ears. The sweet spot was wider and deeper and the sound more focused. One reason for this could be that way that the two products measure room response and compute room nodes, which is slightly different.
Having that, I think that the DSPeaker Anti-Mode 2.0 is a very good product, especially at it's price point, and will certainly meet or exceed the expectations of the average user. And the analog inputs are a big advantage for those of us who favor the vinyl god.
Note that Dirac announced late last year that they were going to release the DHP (Dirac Hardware Processor) appliances. These are standalone units, similar in function to the DSPeaker but running the Dirac application. The announcement specifically mentioned separate versions (DHP-A & DHP-D) for analog and digital inputs, and my understanding is that the devices will not include the Dirac software license, which must be added separately. As far as I can tell, this product has not yet been released and there is no mention of it on Dirac's web site.