External Editor - Availability and/or Requiredness
Haken Continuum/Expressive E Osmose seem to require an external editor to access functionality. Osmose looks like it will have performance controls available on the screen but it is unclear how deep it can edit. And it’s probably not going to be able to reduce down the giant matrix in the editor to fit.
Aodyo Anyma Omega/Waldorf Iridium/Hydrasynth all have hands on interfaces that should allow for editing without requiring a computer.
From my understanding the Anyma Omega will also have a computer based editor available as well (the Anyma Phi had this).
There are certain things like patch management that’s just going to be a fair bit easier on a computer but a required workflow with an external editor definitely makes it less of an immersive hands on workflow.
Signal Chain
I’m not familiar with the Waldorf Iridium but from my understanding both it and the Hydrasynth still follow the traditional oscillators -> filters -> effects sort of path.
Anyma Omega has a bit less traditional more modular design so you can plug and play whatever you want after the oscillators (within constraints).
Haken Continuum/Expressive E Osmose have a fairly nonstandard matrix configuration which goes even more modular than the Anyma Omega. Probably has some things it can do that others can’t but the increased routing likely comes with increased complexity.
Physical Modelling
I don’t think I’ve really seen anything physical modelling with the Hydrasynth.
I believe the Waldorf Iridium has some mechanism for physical modelling but I’m not sure.
Anyma Omega has a bunch of physical modelling mechanisms and resonators that can be combined as modules. I believe they are largely based on stuff from Mutable Instruments.
Haken Continuum/Expressive E Osmose has physical modelling mechanisms. I think at a glance it appears they may go a bit deeper than the Anyma Omega.
The biggest point in the Eaganmatrix’s favour is it has over a decade of preset design so there’s a fairly well rounded set of deep presets vs the limited amount currently available for the Anyma (hopefully that changes for the Omega).
Either way the Anyma/Eaganmatrix engines seem to have a fair bit of overlap in this area.