one of the things i like about alliterative verse is how natural it feels rhythmically, how lifts and dips are defined not in terms of alternating stressed and unstressed syllables but rather where the overall natural emphasis of a phrase lies
i think there is some truth to the idea that alliterative verse feels particularly well-suited to capturing the rhythm of english in poetry (but also i think that most poetic forms (including free verse) each capture a different facet of the language and no one form is the "best")
the website (note: dubious opinions ahead on that site) i looked at to learn about alliterative verse also made the interesting observation that arguably, alterative verse has a similar relationship to free verse that rhyming verse does to blank verse