I am a native English speaker, but not an Hibernian--my father is British and Mother is American. I was born in the Appalachians in Pennsylvania, a peculiar region itself in terms of poetic production.
There are two basic aspects of poetry: the word poetry that can be heard, and the thought poetry that is felt.
I always try to find out as much as possible of the poet's background, because the object of writing in general, and poetry especially, is to reproduce in the reader (at least) part of some experience, feeling or thought that exists or existed in the writer. This is very difficult to achieve with translation, because in many cases the word poetry is meant to play an integral part in conveying the feeling; it is nearly impossible to reproduce the same phonetic rhythm in another language, and even if it is achieved, it will rarely produce the same effect in a mindscape that has been shaped (and, in a way, created) by a different native language.
This phonetic rhythm is important even it is not tantamount; although its absence can impede the capture of the full poetic effect it cannot prevent it, and it can actually teach you a great deal about the poet's native tongue (as @BoldBen pointed out).
The sound of each vowel is part of the wonderful variety that allows us to distinguish Walt Whitman from Gerard Manley Hopkins, or Kipling from Dr. Seuss!
Hannah Brooks-Motl (https://www.cprw.com/Misc/usbrits.htm) says, in part:
W. H. Auden’s introduction to the Faber Book of Modern American Poetry (1956) is almost wholly consumed with teasing out the differences between the two cultures’ verse. “From Bryant on,” he declares in the first paragraph, “there is scarcely one American poet whose work, if unsigned, could be mistaken for that of an Englishman.” Auden sees the defining characteristics of American poetry to be diversity (“no two poets could be more unlike each other than Longfellow and Whitman”), an uneasy relationship with nature (“in America, neither the size or condition or climate of the continent encourages . . . intimacy”), a restlessness that skewers the human relationship to both the past and the future, and a slightly self-deluded belief in the terms of its originality (“There is indeed an American mentality which is new and unique in the world but it is the product less of conscious political action than of nature, of the new and unique environment of the American continent”). These attributes stand in contrast to British poetry which prizes continuity, cozy landscapes and the longest view possible of literary tradition, so that the contemporary poet, laboring at the wrong end of the telescope, knows himself likely to be very insignificant indeed. Auden quotes Eliot’s famous tradition quip, but to ironic effect: “He [any European critic] would not, of course, deny that every poet must work hard but the suggestion in the first half of the sentence that no sense of tradition is acquired except by conscious effort would seem strange to him.” Auden is making the point that American poets, who must earn their long views, are more likely to feel themselves “a literary aristocracy of one.” That is, they write in their own peculiar vacuum...
All that being said, it is perhaps true that the differences are fine enough that only a native of one or the other would tend to notice them in many cases. To a white sheep, all black sheep look alike!