Arrange them in order, according to how much the person enjoyed them.
Then divide the 36 shows into two sets of 18.
Set Two will contain the "better" shows. And the show in question is one of those better shows; though not necessarily the best, or even "one of the best".
If you arrange them in order, the first one in the list would be the best one he has seen. It would be in Set Two, but, you know that although it is among the better ones, the first one is the best one..right?
better and other comparatives are used when comparing two things. best and other superlatives are used when comparing more than two things.
Since the example clearly compares more than two Broadway shows, I would conclude that this is not a use of a comparative form strictly for the purpose of comparison. Instead, it is an example of the comparative form us
On my first reading I thought the meaning was that the person really doesn't like Broadway shows, and is sneering at them a little with this comment. He wouldn't describe any Broadway show as 'one of the best' as he doesn't think they are good enough to be called 'best'. so 'better' is used to show that this is 'best of a bad lot'.
i.e. imagine a snooty ballet reviewer having to comment