Phase Coherence or Time Alignment: Which More Imp?

This thread is really a follow on from a prior one that I let lapse. Thanks to everyone who contributed and helped me to better understand the importance of crossover design in building a loudspeaker. What I gathered from the last thread that there are opposing camps with different philosophies in crossover design. Leaving aside for a moment those that champion steep slope designs, my question is for those who have experience with speakers that are time aligned and/or phase coherent (using 1st order 6db per octave crossovers). Which is more important, phase coherence or time alignment? In other words, which more strongly influences the sound and performance of a loudspeaker? The reason I ask is because of the four speaker lines currently on my shortlist of floorstanders, three are either phase coherent or time aligned or both. The Wilson Benesch Curve's/ACT's and the Fried Studio 7 use 1st order crossovers but do not time align the drivers through the use of a slanted baffle. The Vandersteen 5's and the Quatro's both time align the drivers and use 1st order crossovers. I guess what I am asking is do you need to do both or is the real benefit in the crossover design? I'd appreciate your views.
BTW the other speaker is the Proac D25 and D38