andy2,
In my personal experience, my emotional engagement with a speaker is not based on whether it's first order or not. I have several speakers using high order topologies that I find very emotionally engaging. (In fact, I was partially driven back in to high end audio by how smitten I was with my old pair of Thiel 02s, which are not time/phase coherent).
I was listening to my Waveform Mach MC monitors over the last week. Waveform, when in business, made a pretty explicit rejection of the case for time/phase coherence claiming even frequency response/even power/dispersion and other characteristics were more important for accuracy and believability. Just as I find the Thiels make a good case for the Thiel approach, I find the Waveforms make a good case for that approach. The Waveforms sound to my ears warm, open, extremely natural in instrumental timbre, and particularly uncolored and "alive" sounding. I almost bought a pair of the larger Mach Solos that were for sale recently and I'm kicking myself that I didn't as they are super rare and gone now. (I would not sell my Thiels to buy them, though).
I would go back and forth between the Waveform and the Thiels. The Waveforms are imaging monsters, and the Thiels are great too. In some ways I found the Waveforms a bit more neutral than my 2.7s, and a bit more revealing of exact differences between instruments, and more revealing of dynamics to a degree. So they really communicated a "live" sense of musicians playing instruments, with amazing imaging.
On the other hand: The Thiel 2.7s - certainly having an advantage of being more full range and not just monitors like the Mach Mcs - had that special Thiel thing of organizing the sound even more precisely so instruments and voices have a depth, dimension, solidity and body that the Waveforms did not have. There were more subtle advantages the Thiels gave in the richness - so a flute would have more body and airy texture vs a clarinet, where on the Waveforms both those instruments had a more similar "hardened" quality.
But my point is, I found that the two design philosophies were fairly neck-in-neck in terms of pleasing and impressive results. Which is why I love having different speakers.