When I saw the revival of Spring Awakening I thought the Atkinson had amazing acoustics. Part of that may have been Gareth Owen's brilliant sound design (the man should be designing everything given his level of talent!) but it seemed sound moved throughout the theater (again, might have just been creative speaker placement) a bit better than other shows I've seen. I haven't gotten a chance to go into the Lyceum to check it out for myself during a show, but I imagine that a house that old has amazing acoustics - especially since it was around eons before electronic sound systems. It would've had to have been designed for acoustics - even if performers used to project loudly before mics - so that the audience could hear every line of a show in that age!
I think the only people who could actually answer this question are sound designers who have worked in multiple Broadway houses, and I don't think those guys post on here.
That having been said, I can say that the Marquis is one of the very worst theaters in terms of natural acoustics. It is absurdly dead due to the carpeted walls. This may be a good quality for a vocal recording booth, but it's bad for Theatre. Here's Mick Potter talking about it briefly, in extremely polite terms.
Didn't know that about the Marquis - don't want to denigrate the guy behind that carpeting choice, I'm sure he had his reasons, but it's a shame that a newer theater like that wasn't designed better given the advents in sound design they knew about when the hotel went up. Loved the article from Mick Potter that you linked though! He's another, like Gareth Owen, who knows what he's doing. I saw Phantom in '08 before they took out the old system, and saw it again in January of '09 with Potter's system in and it was a completely different show! Wasn't crazy about some of the stuff he changed, but I have to give the man props for what he did with vocal clarity - Carlotta's voice seemed to soar from the stage, and the scenes in the manager's offices (there's a ton of simultaneous singing and speaking from multiple performers) weren't the easiest to hear with the old system - you could hear every line in Prima Donna with the work he did.