This will just be my opinion, and I may ramble a bit.
The D'Appolito configuration, "MTM" (midwoofer-tweeter-midwoofer) offers the theoretical advantages of vertical symmetry, more midwoofer cone area (plus a second voice coil) for improved dynamic capability in that frequency range without resorting to bigger cones, and better floor-and-ceiling interaction. Imo the main disadvantage is that if you are at the wrong listening height, there will be two different arrival times from the two midwoofers, which can degrade clarity and/or imaging. If the crossover to the tweeter is low enough (say below 1 kHz or so), this does not matter as much as it otherwise would. Very close driver spacing also helps. The most crossover-lobe-free MTM configurations use odd-order crossovers, so the devils are in the details, and my understanding is that this is one of the many details John Dunlavy got right.
The narrowed vertical pattern in the midrange region reduces the MTM's interaction with the floor and ceiling. At lower frequencies the significantly different heights of the two midwoofers staggers their floor-bounce-dip frequencies, assuming their response extends that low.
"TM" (tweeter atop midwoofer) has the advantage of only a single arrival time from the midwoofer, so it is more forgiving of a wide variety of listening heights from that perspective, but may have crossover lobing in the vertical plane that still degrades sound quality for standing listeners. Getting all of these little things right can include a juggling of tradeoffs.
"TMM" is most often seen in "2.5 way" speakers, where the lower midwoofer's top-end is rolled off. This is often seen in narrow-cabinet speakers, where the additional low-end contributed by the bottom mid woofer is used for baffle-step compensation (something I'm not a big fan of). In cases where the two midwoofers both run all the way up to the crossover frequency, their effective acoustic center is much further below the tweeter than is normally the case, which should be taken into account in the design (perhaps by using a tweeter that goes unusually low).
An imo rather elegant alternative is the Coaxial, but it's not easy to get right. Andrew Jones comes to mind of course, but Mark Seaton does outstanding work in high-output coaxials. One of the things these designers both do right, in my opinion, is that they hand off the lower frequencies to dedicated woofers - ime this is especially critical with a coaxial. And getting a midwoofer cone to behave as a benign wide-pattern horn or waveguide requires intelligent tradeoff juggling. But the payoff includes coherence from virtually any reasonable listening angle, horizontal or vertical.
...I believe more than maybe anything else in high-end audio, that implementation trumps theory.
Well said. This is definitely the case here.
At the moment I have three designs in the pipeline, and it just so happens they include an MTM, a TM, a TMM. The MTM is for a recording studio wherein the speaker/listener geometry is known in advance, and the other two are for home audio. To be more precise, what I'm doing would probably be called an MHM, an HM, and an HMM, as I use horns rather than conventional tweeters. The MHM and HMM formats are arguably attractive for theoretically allowing better radiation pattern matching with rectangular horns, while the HM format is arguably better suited to a round horn, but once again the devils are in the details.
Duke