Not really. The implementation matters more than anything else. Heard good implementations and bad implementations of all of these.
Soft domes have the advantage of having very controlled breakup modes and low mass, but maybe aren't nearly as pistonic in their passband as hard domes. The driver Kali chose is quite good in terms of distortion characteristics; the one on the JBL 300 series is not great.
• Barefoot’s radiator tweeter
Ring radiators are a subset of soft domes; they have generally improved HF linearity (often extending up to 30-40k) but behave as though they are a larger diameter than they are, so they beam early. The tweeters Barefoot uses beam around 5k on a flat baffle where a normal dome on a flat baffle is more like 8-10k.
True ribbons have very wide and even horizontal dispersion with very narrow vertical. They also have limited LF capability meaning they generally need to be crossed pretty high.
AMTs (AKA "folded ribbons", "X-ART Tweeters", etc) have better LF capability meaning they can be crossed at a relatively normal frequency range, but can have both distortion and response linearity issues. They also don't have the spectacularly broad dispersion that true ribbons do. Cheap ones suck; good ones are expensive. HEDD's are among the best.
I don't think it actually does anything. They use a standard soft dome. Also hated every PMC I've ever used, so there's that.
• Amphion’s Titanium tweeter
Metal dome tweeters (and make no mistake, an inverted dome is still a dome) are more pistonic (read: lower distortion) in their passband than soft domes, but are much more prone to having wild and uncontrolled breakup modes. The frequency of that resonance depends on the material and the size; titanium, aluminum, and magnesium all are between 25-30k somewhere where beryllium is up around 40k.
Amphion's unique thing is their unusually good vertical dispersion behavior; this is from a combination of waveguide design and crossover placement (it's pretty low, around 1500hz).
Focal's unique thing is that the inverted dome design has unusually wide dispersion characteristics for a dome, often linear out to 75-80 degrees off axis.
Horn-loaded compression drivers are a totally different beast to the rest of what you mentioned, as they aren't direct radiators. They're significantly more efficient (generally up around 100dB/W) and can often be crossed quite low. Disadvantage of course is they're far less common and require a pretty deep horn loading to work properly - and horns/waveguides have their own problems that require careful design to not cause diffraction issues.