In the first essay, Tolkien was arguing that Beowulf should not just be mined for historical facts and philology but should be judged as poetry. It is probably the most influential essay on Beowulf. In it, he declared that the poet's theme was "man at war with the hostile world, and his inevitable overthrow in Time." This makes it essentially a pagan poem, even with the Christian veneer because the man of faith can triumph over death and win everlasting life. Tolkien cited the Northern gods who know that, in the final confrontation between them, their human allies and the monsters, they will lose but they go out to meet their foes with courage anyway. There is something poignant and beautiful about it: going out with your head held high even if there is no one left to sing a song about it after.
It bears the mark of the words of Byrhtwold at the Battle of Maldon, which Tolkien also cited, "Thought shall be firmer, heart shall be the keener, mind shall be more resolute as our strength grows less."
The second essay is also interesting. I am aware that there are many words in Beowulf that exist only in Beowulf and so are not completely understood. Anybody who has undertaken to translate a written piece from one language to another knows there are implied meanings in words that translation often loses and this is the case with Beowulf. I am enjoying reading it but I get the sense that, although I am reading it in the Anglo Saxon, that my understanding of what the poet is saying is rather incomplete.
Tolkien did not write essays for publication in academic journals, the mainstay of any career in the universities today. His 'essays' tended to be lectures or lecture notes. What a shame. He seemed to be more in tune with the heart of the Beowulf poet than any other critic and probably understood him better.