First off, both of these stories are most likely elaborations on the the biblical genesis story. Both of the authors were Christians and no doubt had interesting views of how it all began. The theme of music is shared by both is used as the method of creation. No doubt both men had visited cathedrals and heard choirs of voices resounding throughout the massive buildings. The view of creation as a beautiful harmony seems almost natural if you have heard certain masterpieces. The instrument of the music is different in each. In [A] the Ainur are created by Iluvatar (represents God) and they in turn sing the part of the song that was put in them. In [MN] the singer is a singular person in the lion Aslan (represents the Christ, son of God). The Lewis version of having the Son involved in creation reflects thoughts presented at the beginning of the gospel John. John chapter 1 verse 3 states
Through him all things were made; without him nothing was made that has been made.Aslan therefore is the personification of this scripture. Tolkien's presentation could be best described as God creating angels and giving them a purpose. Those angels then fulfill their purpose in creating.
The literary style in [A] is much closer to the actual biblical account of creation than [MN]. Tolkien himself was a linguistics professor and wrote many languages for his books. This knowledge of the origins of many languages most likely caused him to write a structured and believable account of creation. For his writing style can easily be seen to closely mimic ancient stories from almost all origins. This style can be perceived as distant or detached to some people, but it is nonetheless accurate from a historical standpoint. Lewis on the other hand uses [MN] to take the reader to the date of creation and makes them an observer. The creator seems much more personable. He even laughs with creation. Most people tend to prefer this version because it seems more personable and fits better with modern times.
The timeline presented by Tolkien is somewhat vague. For an unknown amount of time creation was occurring being designed. The actual creation process in his account takes many centuries to complete. Lewis has the account occur in a singular day and would fit more literally with the Genesis account. I think that you also have to take into account the intended audience. While Lewis's audience was explicitly stated to be children, Tolkien's book takes on a much more scholarly take. This take presents a much more serious and intricate look at things than a mere children's book would.
Taking all things into consideration, it is hard for me to choose a favorite. Although from a personal standpoint, [MN] gives me a much better feeling.