Phase Coherence or Time Alignment: Which More Imp?

Partially true. In a hurry today so I'll be brief and general.

Time alignment generally refers to the alignment of the theoretical point sources of all drivers in a cabinet, such that the signals emanating from them at one moment in time all reach your ear at the same time. The sloped or stepped baffle tries to accomplish this - but of course, if you're not at EXACTLY the right seating height for that particular geometry, and EXACTLY the same distance from both speakers, and have no near field room reflections, much of the benefit is lost.

Phase Coherence problems are mostly created by crossovers as they split the frequency bands. So a time aligned speaker is no more likely to be phase coherent than any 2 or 3 way speaker, unless much care, measurement and testing and re-testing and re-testing goes into the crossover design. Without that - even though what's leaving the tweeter and the woofer may arrive at your ear at the same time, the signals from each have probably lost their phase "alignment" while travelling through the crossover and drivers.

There is some dispute over whether you could actually hear this if a crossover had a true infinite slope. But since the reality is that there is large overlap in the midrange where the woofer and tweeter are producing the SAME frequencies, if they're out of phase with each other it's bad news. In a worst case scenario, in an anechoic environment, they could perfectly cancel each other.

Not a thorough explanation but I have to run. I'll bet Roy frm GMA has expounded on this somewhere already.

I have to agree with Lrsky, although I usually prefer not agreeing with anyone. The theories of speaker designs are interesting, but the actual experience is what matters ultimately. All speakers are compromises - and overall it's pretty amazing that you can etch a pattern into plastic with a cutting head, play it back with a tiny diamond, amplify that signal a gazillion times, and then have it come back at you sounding ALMOST exactly like it did going in.

I've heard many of these new "wonder-speakers" with all sorts of expensive drivers and internal wires that are just unlistenable (to me), and I've heard 20 year old designs with some updates (like my Dahlquist DQ-20i's) that keep beautiful music sounding that way. And despite whatever a designer does with Phase and Time, room interactions play a huge, huge part in what you'll actually hear.

I have heard both Joseph Audio Pearls and Green Mountain C-3's a fair bit and they're both great speakers with different attributes for people with different "ears".
I had a trade pass at the last HES San Francisco and went back and forth without having to wait on lines between Joseph Audio and Avantgarde Trios and came to the conclusion that if I had to live with one or the other at home, I'd pick the Pearls as less fatiguing - not what you would predict for a steeper slope crossover.
I also have spent a few hours audiotioning GMA C-3's and found them to be spectacularly dynamic, very detailed, and also a bit bright/forward in the mids (for my taste) - also not what you'd predict from a 1st order design.

So go figure...