Here's the melody to which "Brightest and best of the sons of the morning" is sung in "Star in the East" (one of the lyrical differences is "sons" in place of "stars"):
(As the name would suggest, Anonymous 4 features four singers [and four vocal parts]. I did my best to isolate what I think is the main vocal part here.)
Here's the melody to which "Brightest and best of the stars of the morning" is sung in The Lutheran Service Book (the tune is "Morning Star"):
For both, the notes to which "brightest" (the first syllable, anyway) and "best" are sung have greater values than the surrounding notes (half notes amid quarter notes), and those greater values provide even further emphasis to the superlatives. In "Star in the East," those notes have the highest pitches in the phrase, which also emphasizes the superlatives.
While looking at the hymn, I also noticed something about the second phrase:
In the second verse, the text here is "Low lies His head with the beasts of the stall," and there's a descent in the melody that musically represents "Low lies His head."