Several of the Inklings were poets; and all the Big Four - CS Lewis, JRR Tolkien, Charles Williams and Owen Barfield - began their literary careers intending primarily to become poets; only Williams ended his life regarding himself a poet.
Williams was the only successful poet among them; being regarded as one of the leading British poets of his generation; albeit mostly for the poetry that was published before Taliessin Through Logres and The Region of the Summer Stars - which Williams himself regarded as his best and only significant work.
At the other extreme, it has been said that Tolkien is, because of the songs and verses in The Hobbit and Lord of the Rings, the most often read of twentieth Century poets (this is assuming that the verse is not just skipped by readers - as has been suggested).
Tolkien wrote a great deal of unpublished poetry in his early years (including unfinished long poems), published quite a few shorter and comic or lyrical works, including translations and modern-language development of ancient works, mostly in small magazines.
Lewis's first two books were poetry - and it was only the critical and sales failure of Dymer (when he was aged about 28) that he decided not to continue on that line; although he published many more verses in magazines through the rest of his life.
Barfield wrote considerably more poetry than he published; but he did publish in small magazines - mostly later in life.
But which was the best poet? Williams seems like the obvious candidate; but I do not regard Williams as a real poet. And to my inner-ear; Lewis and Barfield were also 'contrived' versifiers; whose work lacked that something unique to real poetry.
So there is no doubt in my mind that JRR Tolkien was the best Inklings poet - indeed the only real poet among the Inklings if judged by the standard of English lyrical poetry (i.e. song-like verse, plus something more) that defines for me what is 'poetic' about poetry.
If I was asked to define what makes real poetry - as contrasted with verse - I could only do so indirectly; for example by pointing out that Palgrave's Golden Treasury (1861) displays the nature of this tradition in a very pure and concentrated form.
Most of Tolkien's output would best be characterized as verse; and it varies pretty widely in quality (as does the work of most real poets) - but Tolkien at his best was a real poet; whereas the other Inklings were writers of verse, and not true poets.
My selection of Tolkien's poetry at its best would include these five poems; The Sea Bell; Imran; and Aotrou and Itroun - and also some others, including a few of the earliest poems posthumously published in Lost Tales.