This is a time when Frank was writing faster than he could release albums. The whole Lather debacle threw things off, 1977 was the first full year of no new Zappa albums since 1965. This album was recorded in 1976, same year that Zoot Allures was released, and released in 1978, by then Frank was working on Shiek YerBouti material already, and had a new lineup. But anyway...
Zappa In New York is definitely one of Zappa's best albums. It has a BIG sound, very orchestral, but also filled with jazz, humor, and prog. All these Lather albums (ZNY, SD, ST, and OF) are the last albums featuring any of the early-mid 70s members (George Duke, Ruth Underwood for example) but also feature musicians who would continue to appear on later albums (Terry Bozzio, Patrick O'Hearn) so this era is kind of a best of both worlds. We get everything here.
ZNY overlaps with Lather, but there are cuts here that don't appear on the mammoth 4LP set that never came to be. The live Sofa is the best version, and The Black Page #2 is some epic music, to say the least; this is the best version. I Promise Not To Come In Your Mouth is actually the title track from Lather but the same recording. It should be noted that the songs that do appear on Lather have different cuts, and overall different mastering. (ex. ZNY sounds brighter)
Bozzio is a mad man.
Bozzio is a mad man. Listen to this guy play drums. Vinnie Colaiuta may have had the most dexterity, and maybe a couple of Zappa's earlier drummers had more jazz influence, but Terry Bozzio knew how to rock-the-fuck-out AND had the chops to back it up. He also brought some humours vocals to a few albums as well.
I agree that Zappa didn't so much rearrange a song just because he could, but in order to bring out the best in his lineups, and sometimes the live versions are better with Zappa.
I usually end my post on each album with related albums from the same time period that were (usually) released posthumously, but with this period, there's too much overlap between music Frank was working on live while these albums were coming out (Shiek, Joe's Garage material) and the fact that the Lather albums contained different lineups spread across different eras that it's too confusing and/or a spoiler for upcoming albums (if you care enough). The only thing I can say is Philly 76 because ZNY is also from 1976 and has a similar, but stripped down, lineup and with occasional female vocals.
Here's some more interesting facts about this era. Look at what was supposed to be released in 1977 before Zappa In New York:

It looks like the cover of Joe's Garage. Let's take a closer look...

This era is one of those times where, even if just slightly, things went Zappa's way, the remaining discography may have been COMPLETELY different from here forward. For better or worse? We'll never know, but Zappa did get way more cynical after the Lather fiasco.