If you ask me...
1) All minimum phase filters (that's more than 90% of filters you see) with the same frequency curve without added distortions sound the same. There is are no magical "EQ algorithms" that would make EQs sound different without added distortion or different frequency curves.
2) Some EQs are based on some specific hardware units. If they are, it's clearly stated somewhere, like those made by Waves, which seem to usually have 2-4 first harmonics. That means added distortion, nothing magical, very easy to implement.
3) Linear phase filters sound somewhat different from minimum phase. Apart from that, phase doesn't matter because all minimum phase filters have the same phase behaviour. You can add so called all-pass filters that change the phase, but this is inaudible unless you mix the original sound with the filtered.
4) Minimum phase filters can be made to sound the same. Some EQs have different filter shapes (URS N-series comes to mind) so you may need two or more filters of different shape to approximate it. For example, you could use one shelf and one bell filter to approximate a "pultec-style" shelf. The only difference is in the frequency domain.
5) When a minimum phase filter is said to be specifically "clean" or "accurate" it probably only has to do with the usual problem of that normally digital filters have +-0 difference at half of the sampling rate (like 22050hz) and that leads to less boost or cut at e.g. >18khz.
So, if someone comes to me and says that he has a new EQ design, I would ask him which is it: new filter shapes or added distortion. Most likely it would be just a new GUI.