Cædmon was from the abbey at Whitby, so it is undoubtedly Northumbrian originally.
Unusually for an Old English poem, we have many copies of Cædmon’s Hymn, seventeen* manuscript versions have survived, four in Northumbrian, thirteen in West Saxon. The poem only survives, however, because Bede mentions it in his Ecclesiastical History and provides the opening lines in Latin. Given the huge number of Bede manuscripts that survive, it’s no surprise that many copies of Cædmon’s Hymn also survive. Five of the surviving manuscripts are West Saxon translations of Bede’s Latin and contain West Saxon versions of the poem. In all but one of the others, the Old English version is copied as a marginal or interlinear gloss, in some cases added later, in others the gloss is copied by the same scribe who penned the Latin. In one Latin version, a West Saxon translation is included in the main text, but this is a fourteenth century manuscript, quite late.
The oldest of the manuscripts, Cambridge, Cambridge University Library, MS K.k.v.16 and St. Petersburg, Russian National Library, MS Lat. Q.v.I.18, both mid-eighth century manuscripts, some seventy years after the poem was probably composed, are Latin with a Northumbrian gloss. In the Cambridge manuscript the Northumbrian version is added at the end of the manuscript; in the St. Petersburg copy, it’s a marginal gloss to the folio containing Bede’s Latin version of the poem. Both glosses are copied by the scribe who penned the Latin, probably at the same time as the main text was copied.
The surviving poem is incomplete, as Bede only translated the opening lines into Latin, and all the Old English versions include only the portion that Bede translated. Also, it’s not certain if the Old English versions are re-translations from Bede’s Latin, or taken from an Old English original. Most scholars tend to accept that it’s not a re-translation, but I have my doubts. The poem looks like it’s been run through a translator several times. The only reason anyone pays attention to it is its origin story and the fact that it is one of earliest Old English poems we have. (The portions of the The Dream of the Rood written in runes on the Ruthwell Cross were inscribed at about the same time as the oldest manuscripts of Cædmon’s hymn, so these two vie for the title of oldest. The Dream of the Rood is a far better poem. Cædmon’s Hymn, quite frankly, is crap.)
* Actually, one of the manuscripts was destroyed in the 1731 Ashburnham house fire, but we have a sixteenth-century transcript of it. And in two others the poem is badly mangled by the scribes, and are often discounted, leaving some counts of the number of surviving manuscripts at fourteen.