Two productions that I thought were very different between Boston and NYC, 40 years apart, were Dear World and Finding Neverland. Dear World received mediocre reviews in Boston and managed to eliminate some of the best stuff. It was very different an a lot worse. There were so many things to love, but the show went from a B (with some beautiful A quality scenes) to a C- (while still having some lovely moments). I have always wondered what would have happened if they staged the show in a small theatre and eliminated the incredibly stupid (but incredibly catchy) title song. I imagine Lansbury would have not been part of it, and she was the one outstanding thing about it.
Finding Neverland changed dramatically...I thoroughly enjoyed it in Boston (Cambridge), but I HATED the choreography, which was very prominent in the original production. The choreography was very different, at least as I remember it, but still not good. Interestingly, I recently saw the road tour, and the first 20 minutes or so were totally different from either earlier version, and far inferior to both. I still enjoyed the shows because of its heart, individual numbers, the great staging to the recreation of the play, ending with Sylvia's death...IMO a great scene in a less than great show.
I don't know if the show changed dramatically beyond the opening number, but Broadway legend has it that A Funny Thing was headed to failure until they added the opening number, Comedy Tonight, which -- besides being a great number -- told the audience loud and clear that they were in for a lot of silliness and to 'let their hair down'. And apparently Hello Dolly opened in Detroit (or am I remembering this incorrectly) without a title number and was not received well. While HD would not have been as good without that number, it would have still been a lot better than a lot of hits in those days; so, I can only imagine that a lot of changes were made post opening in Detroit, besides the title number. But this is just conjecture.