Still relatively new down this road. My understanding is that the DEQ has an FFT so you can do sophisticated functions, not just fancy tone controls or parametric equalization though it can do that too.
I am not aware of the DEQ performing any other than standard EQ shaping filters such as parametric, shelving and graphic(which is simply a series of precision designated notch/peak filters).
However, the DEQ has a flashy FFT display/analyzer function for room measurements when you attach a measurement mic.
The DCX on the other hand, works more like a fancy crossover. By working in the digital domain you avoid some phase problems that affect LC crossovers. You are limited to 3 filter functions if I recall correctly.
It should be cautioned that standard filters are
usually preferred in practical application. If say you correct a specified minimum phase response peak of the actual loudspeaker(not a non-minimum phase error), which of course, most speakers have some characteristics that could be improved, then the counteracting filter such as that an analog EQ(and the DCX is designed to mimic, as well as the DEQ) produces nulls the reverse amplitude and phase error. The DCX and DEQ use IIR digital filter types. Now, the other kind of digital filter is the FIR filter; functions that can produce amplitude changes while not affecting phase for example, or alter phase in ways not normally possible otherwise. However, the reality of this is that it would not then correct the phase error along with the amplitude in the example given above of a minimum phase speaker response error. And if you wanted FIR for the crossover functions themselves(say to use extreme rate rolloff slopes without phase shift), realize that the desired phase perfect response only works closely on design axis of multiple integrated drivers on a speaker. As you move off axis, the filters do not any longer have the predicted properties, since the drivers change their FR and phase response as you move off axis, and severe pre-ringing artifacts can contaminate the off axis response of the speaker. Refer to this link and scroll down to 'digital crossovers':
http://www.linkwitzlab.com/frontiers.htm#I
For say LF correction of a room; this is more or less minimum phase situation, and the analog-like phase change with a standard corrective parametric band is desired as it nulls the phase change in the minimum phase error.
Now, there may be some cases where FIR is beneficial, but it would probably be most so in an environment that has unique problems that need to be addressed in other ways for optimal effect(such as having a decent/good acoustic environment to begin with instead of trying to use extreme correction methods on the signal). One could for example improve SQ on a very narrow listening window by counteracting some extreme room artifacts in the full bandwidth; but better results would be had by addressing the actual room itself rather than depend entirely on signal manipulation.
The DCX also has dynamic EQs, etc. Now, the DEQ's features not found on the DCX are the stereo expander, the graphic EQ(but since this is just a collection of notch/peak filters - they can be manually entered into the DCX's parametric filter.
If the DEQ does have FIR filter types in some capacity, I am not aware of it.
