The part that I noticed specifically is the music that accompanies the word "everywhere" in the lines "Go tell it on the mountain / Over the hills and everywhere." I think the Simon & Garfunkel version treats this much better in relation to the text.
As far as I can tell, this is the music for everywhere, given as the individual parts and together:
There are two things here that I think are significant as far as the text. First, Paul Simon's part sort of looks like the titular mountain. Second, the parts are moving in opposite directions. Garfunkel's moves down and then ascends; Simon's rises and then falls. So, between the last two notes, there's an expansion in the parts, which helps to reflect the lyric - "Go tell it on the mountain / Over the hills and everywhere." Garfunkel goes to the higher registers, and Simon to the lower.
The notation for the music as it appears in both Lutheran Worship and The Lutheran Service Book looks like this:
Additionally, the phrase in Porter's arrangement (in G major) ends on a G, so there's a feeling of completion. But if the invocation is to "tell it... everywhere," it seems as if that phrase shouldn't resolve so soon. Simon & Garfunkel's (which I'm pretty sure is in F major), ends that phrase with a C and an E. There isn't any resolution there, implying that the telling still continues.