Look, I am not going to dispute the greatness of Seamus Heaney, or his awesome, magical rendering of Beowulf. Part of its magic lies in how modern he made the poem. The thing is though that it is translation or a paraphrase. Alexander's poem is more of a modernization, rather than a translation. You are basically reading the original Beowulf, with the words updated in their spelling, or replaced when necessary with more modern words where the old ones are no longer comprehensible. He of course preserves the alliteration as much as possible, and the lines remain short. To me this method leaves the poem as it was, and merely transforms its dialect from that of 11th Century Wessex to modern international English. To be sure, this method demands more of the reader than a paraphrase does, since you have to figure out what the swan's road or the whale's way, and kennings (riddle-names) like these are. So, if you are really intrigued by this poem, which must have been intended to be the monument of its civilization, especially when you think of the number of sheep they had to kill and the expenses involved in preparing their skins, and the fact this story concerns what was supposed to be the greatest hero in the most heroic age of man, then you will want to read Alexander's rendition.
As for why you would want to read Beowulf in whatever edition, the main thing is that it is the great poem of the English language. No one will dispute that Shakespeare is our language's greatest playwright, and few would dispute that the prosody of the King James Bible overwhelms that of any other prose work, or maybe even that the Lord of the Rings may be our greatest novel, but for epic poetry, ORIGINAL epic poetry, is there anything like Beowulf in English? It must have stood out in its day as the greatest poem ever, considering like I mention above, the expense involved in its production, and no one has ever since, in English, written a poem so great in scope, and so representative of the experience of English-speaking civilization. Spencer tried, but his allegorical figures hold no mystery - they beat you over the head with their meanings and the moral lessons you, a corrupt creature, are supposed to learn from them. Chaucer, though great too, bundles a collection of tales together about a trip to a church. Milton, who seems to have based his greatest poem on another Anglo-Saxon poem in his friend's collection, is retelling something we can find in Genesis. Beowulf treats the Danish ancestors of the English before they crossed the sea to England. It's a lovely reminder that we in North America are no more separated from the homeland of our language than they of our language's supposed homeland from their own. Beowulf has achieved national epic status in England for good reason, and more than this, it has achieved pan-national epic status for the entire English-speaking world. This is quite the triumph for the resident poet of some Anglo-Saxon king and his many sheep, so long ago. They put in their great effort, the sheep sacrificing their very lives even, to preserve and propagate this awesome work. The poem fought the ravages of time and fire, and is now preserved and sprung anew from the ashes, like the phoenix, to provide great solace and sustenance for us, the Anglo-Saxons' linguistic inheritors, today, in our brief flit though this lighted mead-hall of life.