Outside of both systems 'decoupling' the mix from the playback speaker arrangement, the biggest difference between Atmos and Ambisonics is that Atmos is object based, so some things remain defined as individual elements which play back at specific times and in defined spatial locations all the way to the rendering device in the theater, rather than being a fully pre-cooked mix. That's where much of the value exists in the new formats, for cinema applications at least.
Other than the techniques for recording, one of the aspects I find most interesting and applicable here is this 'decoupling' of recording and storage formats from playback formats. I think that's where the most growth and adoption potential for surround sound lie in general, and more specifically for a wider application of surround sound for music reproduction. Ambisonics has been capable of that from the beginning that’s the way it is almost always used.
Perhaps ironically, the surround recording techniques I've discussed previously in the thread are mostly conceptually simple approaches with direct mapping from microphone channel to speaker playback channel. That direct channel mapping is what presents the biggest problem with playback flexibility. Those techniques and the recordings made with them needn't always be constrained that way though, and that’s the direction forward to greater adoption.
In the commercial cinema world, which drives the surround sound market and where all serious technological developments are focused, Dolby now markets their zillion speaker Atmos system to theater owners, while Barco offers lower-cost 9 to 12 channel Auro theater options, and DTS offers their alternate take on commercial movie theater. All those companies now talk about arriving at a defacto common open standard to simplify the creation, and distribution of film content (or rather ‘digital theater’, as 'film' rapidly becomes an archaic term sort of like us referring to live music recording as 'taping'). They differentiate themselves by marketing their own production tools to creators, while understanding the value of producing output which will work more or less everywhere through any other company’s B-chain reproduction equipment, but also strongly market their own versions of that reproduction gear to differentiate themselves to theater owners. The differences lie at the ends of the chain, the need for common ground lies in the middle. This is the direction things are rapidly moving in the cinema world, and is the reasonable and perhaps inevitable approach as surround sound playback solutions constantly evolve towards more and more complex arrangements at the front and back ends of the chain.
In contrast, the situation of the past 25 years or so has been one of final reproduction formats which are more or less standardized (5.1 / 7.1), but using different proprietary distribution formats specific to each company: Dolby digital, DTS, SDDS. Now the reproduction formats have become different from each other, and it has become beneficial to these companies to provide movie studios and theaters with more of an open common storage and distribution format, while freeing themselves to develop creation and final playback tools where they can differentiate their products. This is a business to business thing between companies such as Dolby, movie studios and theater owners and doesn't directly affect us as individuals but is a positive trend and the trickle-down from this dynamic has the potential to be very beneficial..
Ambisonics already works that way. It exists in all three realms- recording/creation, storage/manipulation, and playback. It is almost never used exclusively for all three, especially playback, at least outside of research institutes and places like science museums. There is no potential for growth of classic ambisonic playback through geometrically symmetrical playback arrays, although there is possibly some application of ambisonic techniques to improve non-ambisonic playback. It can be used for storage, but is only used in the cinema world on the content creation side (recording), so its use as a widespread storage format is unlikely and also less flexible. It is obviously used for recording via ambisonic microphones as well as other direct creation techniques, and in that case is often directly converted to some other form for storage/manipulation and final output (ie: directly from microphone A-format to a virtual 2-channel stereo output for instance through a SoundField microphone controller box or the Tetramic software)
Ambisonics might be best utilized as a simple and powerful manipulation tools for other formats, separate from its creation and reproduction aspects, where the techniques work for stereo manipulation as well as multichannel surround. Ambisionics ‘decoupled’ the recording/creation stage from the storage/manipulation stage and the playback stage from the start, long before other surround formats which are only beginning to do so now.
Harpex exists in this world of ‘decoupled’ formats, as it is specific purpose is to convert and manipulate ambisonic (or other) input to form two-channel stereo or binaural headphone output.
Outside of the cinema, binaural reproduction over headphones is the most likely way for a majority of people to be able to enjoy surround content these days, regardless of whether the content was originally constructed from objects flown around by a mixer on a dub-stage, or recorded with microphones binaurally, ambisonicly or some other way. Yet that same content should be expected to also work in the car, out of the TV, over a traditional stereo system, in the home-theaters of the few that have them, in the big-ticket Atmos or Barco or DTS theaters downtown, or wherever.