Having given this thread alot of thought over the last few months, and comparing the sound of various eqs I own or have demo'd, I have come to the tentative conclusions that:
1) Minimum phase digital eqs with no extras (noise, harmonics, etc.) can sound the same if they use the same coding techniques and one is patient enough to match the actual curves (as opposed to the listed parameters of the interface).
2) Some minimum phase digital eqs employ non-standard coding techniques that impart a slightly different character, which makes it difficult, if not impossible, to match curves with standard (biquad) digital eqs.
Regarding the Eliosis chart, I argue that they are also using 'advertising tactics' to some extent - i.e. they list Linear Phase eqs along with Minimum Phase ones. Linear Phase eqs will sound different than Minimum Phase ones due to the lack of phase shift and the pre & post ringing associated with LP (which varies based on the LP design), and they are CPU hungry by nature. Of particular note in the list is the Algorithmix Orange, which employs upsampling; the Orange is designed to eq as high as 384 kHz sampling rates (DSD), so not only is it LP, but if there is warping of the curves, the warping would (I suppose) be spread out over a very high frequency range. Perhaps if one turns the upsampling off, it will exhibit the same warping characteristics as a biquad mp eq.?. Regardless, all the LPs in that list are
different animals than the MPs.
Although I am no mathemetician or coder, I tried to decipher this paper by Sophocles Orfanidis:
http://www.ece.rutgers.edu/~orfanidi/ece521/hpeq.pdf
It seems that this mysterious 'decramped' or decrampled' curve is the Orfanidis extension of the standard BiQuad curve; if one looks at the Eliosis site, the examples of the Orfanidis curves are much closer to the 'analog modelled' curves than the standard 'digital' curves, which would imply that an Orfanidis curve is a reasonble alternative to the Eliosis MP 'analog like' curves.
Again, an eq (LP or MP) that employs upsampling will exhibit different charcteristic than a non-upsampling eq. The equalization at a higher sample rate exhibits less warping at the nyquist frequency, since the calculations are done with doubled or quadrupled nyquist. Of course this smoother curve in the high frequencies is paid for with the quality of the decimation filter, the quality of the src algorithm and the CPU hit. The UAD Precision EQ has a soft, smooth sound at least partly due to upsampling. And one can see the difference with Voxengo's Harmoni-EQ (and the LP Curve-EQ) when it is switched from upsampled to non-upsampled; in 'normal quality - not upsampled, the visual curve changes to reflect the warping near nyquist).
It seems to me that there are these differences to choose from:
Minimum Phase BiQuad (Standard Digital)
Minimum Phase Orfanidis (Decrampled - in the bell, shelf, pass or all filters)
Minimum Phase (either of the above) upsampled
the mysterious 'Analog-Like' algorithm emloyed by Eliosis (also MP)
Linear Phase IIR (possibly employing one or more of the above filtering techniques)
Linear Phase Upsampled IIR (possibly employing one or more of the above filtering techniques)
and:
LP FIR, which seems a different animal to all of the above, and has its own advantages and flaws (from what I understand, my favorite eq, the Algo Red, is FIR).
Then the designer may have added harmonic generation and or/ noise, which could theoretically be static or dynamic in nature relative to the signal amplitude and frequncy response.
That seems like a lot of possibilites, making the generalization 'all digital eqs are the same' to be a bit questionable.
Know thine eq.
P.S. There is an indication in the Orfanidis paper, if I understand it right, that certain coding techniques lend themselves to static eq settings, and other techniques are better for dynamic changes, which might indicate a potentially different quality for eqs with fixed frequencies, Qs and/or stepped gains, but I don't know enough math to be certain of this point; if anyone can clarify, it would be much appreciated.
P.P.S. Also in the Orfanidis paper, there is a discussion of the rounding errors being related to the number of iterations; I wonder if this means that it is possible to employ a given number of iterations in an MP eq algorithm to obtain a higher accuracy? If so, that would change the quality of the eq, as some designers would choose lower iterations to improve CPU efficiency. But again, I don't know what I am talking about mathematically!