I too mainly know about AZS and Harmonik from postings by people using them. Harmonik either has more users or is better at communicating, I don't know.
To me it appears that both are fairly similar but AZS uses 6 mic capsules in its "full size" model versus 5 capsules in the Harmonik. Whether 6 produces a still better "spread" than 5 I don't know. Harmonik also has a model with double the number of capsules, especially targeting cassotto accordions.
Long before these there was and still is Microvox, which is a completely non-invasive system: everything positioned on the outside and attached with velcro, so it's easily removable as well. Microvox uses 4 capsules (model 420 treble side) and in my experience with it that's just about enough.
I have pictures from a quintet (plus drums) performance in 2012, 4 accordions using the Microvox system (model 420, mounted on a bracket) and the bass with internal mics (the common Sennheiser system). Wer were playing in front of a large castle (at Bokrijk in Belgium), using 2 Bose L1 model 2 units placed behind us (yes, commonly this is a feedback loop nightmare, but not with this setup!).
People came to us from *behind* the castle telling us they could enjoy our performance loud and clear even there. I can tell you that the sound was really loud where we were sitting and playing!
The Microvox system is really great, but... it is external, uses an external "power supply" unit (with volume control), and is thus perhaps a bit more prone to cabling problems. Harmonik and AZS are installed inside and you just plug in a jack (or with the Harmonik Galliano model an XLR cable) and you're good to go.
