One on one
Here are the descriptions of the contenders.
Of the Enemies
Last of all is set the name of Melkor, He who arises in Might. But that name he has forfeited; and the Noldor, who among the Elves suffered most from his malice, will not utter it, and they name him Morgoth, the Dark Enemy of the World. Great might was given to him by Ilúvatar, and he was coeval with Manwë. In the powers and knowledge of all the other Valar he had part, but he turned them to evil purposes, and squandered his strength in violence and tyranny. For he coveted Arda and all that was in it, desiring the kingship of Manwë and dominion over the realms of his peers.
From splendour he fell through arrogance to contempt for all things save himself, a spirit wasteful and pitiless. Understanding he turned to subtlety in perverting to his own will all that he would use, until he became a liar without shame. He began with the desire of Light, but when he could not possess it for himself alone, he descended through fire and wrath into a great burning, down into Darkness. And darkness he used most in his evil works upon Arda, and filled it with fear for all living things.
On the other side of things
Of the fabric of Earth had Aulë thought, to whom Ilúvatar had given skill and knowledge scarce less than to Melkor; but the delight and pride of Aulë is in the deed of making, and in the thing made, and neither m possession nor in his own mastery; wherefore he gives and hoards not, and is free from care, passing ever on to some new work.Those and later quotes are from The Silmarillion, Ainulindalë, JRRTolkien. The next chapter, called Valaquenta, elaborates:
Aulë has might little less than Ulmo. His lordship is over all the substances of which Arda is made. In the beginning he wrought much in fellowship with Manwë and Ulmo; and the fashioning of all lands was his labour. He is a smith and a master of all crafts, and he delights in works of skill, however small, as much as in the mighty building of old. His are the gems that lie deep in the Earth and the gold that is fair in the hand, no less than the walls of the mountains and the basins of the sea. The Noldor learned most of him, and he was ever their friend.
JJR Tolkien immediately links Aulë and Melkor in powers and desires. This is unique: he does this with no other Vala pair. In character, Melko often feigns good will, good works, good intentions and good advice, but Aulë personifies them (and the other buddhist right paths ).
Melkor was jealous of him, for Aulë was most like himself in thought and in powers; and there was long strife between them, in which Melkor ever marred or undid the works of Aulë, and Aulë grew weary in repairing the tumults and disorders of Melkor. Both, also, desired to make things of their own that should be new and unthought of by others, and delighted in the praise of their skill. But Aulë remained faithful to Eru and submitted all that he did to his will; and he did not envy the works of others, but sought and gave counsel.
Thus, Aulë and his works and allies are a special target of Melko. While Melkor is capable of marring anything made, Aulë is capable of repairing it but wearies with that work. Thus, Melkor can continually escape and wear Aulë down.
One on One: Melkor wins.
Team Versus Team
On Aule's Team:
The spouse of Aulë is Yavanna, the Giver of Fruits. She is the lover of all things that grow in the earth, and all their countless forms she holds in her mind, from the trees like towers in forests long ago to the moss upon stones or the small and secret things in the mould. In reverence Yavanna is next to Varda among the Queens of the Valar. In the form of a woman she is tall, and robed in green; but at times she takes other shapes. Some there are who have seen her standing like a tree under heaven, crowned with the Sun; and from all its branches there spilled a golden dew upon the barren earth, and it grew green with corn; but the roots of the tree were in the waters of Ulmo, and the winds of Manwë spoke in its leaves. Kementàri, Queen of the Earth, she is surnamed in the Eldarin tongue.
The Book of Lost Tales gives Aulë and Yavanna an extended family through two Valar children. Their son is Oromë the Hunter, who found and guided the elves to the Undying Lands. His spouse is Vana the Ever-Young, who is also Yavanna's sister. Their daughter Nessa, the Fleetfooted, and Tulkas the Valiant were the only Valar couple to be wed after arriving in Arda. Each of these Valar have their own numerous, mostly unnamed Maiar friends and followers.
On the Enemies side, though
Yet so great was the power of his [Melko's] uprising that in ages forgotten he contended with Manwë and all the Valar, and through long years in Arda held dominion over most of the lands of the Earth. But he was not alone. For of the Maiar many were drawn to his splendour in the days of his greatness, and remained in that allegiance down into his darkness; and others he corrupted afterwards to his service with lies and treacherous gifts. Dreadful among these spirits were the Valaraukar, the scourges of fire that in Middle-earth were called the Balrogs, demons of terror.
Among those of his servants that have names the greatest was that spirit whom the Eldar called Sauron, or Gorthaur the Cruel. In his beginning he was of the Maiar of Aulë, and he remained mighty in the lore of that people. In all the deeds of Melkor the Morgoth upon Arda, in his vast works and in the deceits of his cunning, Sauron had a part, and was only less evil than his master in that for long he served another and not himself. But in after years he rose like a shadow of Morgoth and a ghost of his malice, and walked behind him on the same ruinous path down into the Void.
Melkor undermines Aulë's team by fomenting treason and defection of alliance among them. Here is an except from The Silmarillion Chapter 1 showing how team versus team worked early on.
Now it came to pass that while the Valar rested from their labours, and watched the growth and unfolding of the things that they had devised and begun, Manwë ordained a great feast; and the Valar and an their host came at his bidding. But Aulë and Tulkas were weary; for the craft of Aulë and the strength of Tulkas had been at the service of an without ceasing fax the days of their labour. And Melkor knew of an that was done, for even then he had secret friends and spies among the Maiar whom he had converted to his cause; and far off in the darkness he was filled with hatred, being jealous of the work of his peers, whom he desired to make subject to himself. Therefore he gathered to himself spirits out of the halls of Eä that he had perverted to his service, and he deemed himself strong. And seeing now his time he drew near again to Arda, and looked down upon it, and the beauty of the Earth in its Spring filled him the more with hate.
Now therefore the Valar were gathered upon Almaren, fearing no evil, and because of the light of Illuin they did not perceive the shadow in the north that was cast from afar by Melkor; for he was grown dark as the Night of the Void. And it is sung that in that feast of the Spring of Arda Tulkas espoused Nessa the sister of Oromë, and she danced before the Valar upon the green grass of Almaren.
Then Tulkas slept, being weary and content, and Melkor deemed that his hour had come. And he passed therefore over the Walls of the Night with his host, and came to Middle-earth far in the north; and the Valar were not aware of him.
Only when Tulkas and Aulë are tired and feasted to somnolence, does Melkor and his team act. Melkor's opinion must be that the Valar Lords of the West are capable of besting him in open battle. Indeed, Melkor suffers a huge loss at this same team.
The following battles are not chronicled well, since the historian Elves did not witness them. Indeed, the Vala ensured the Elves suffered no part of it at all. The battle ended thus:
Manwë said to the Valar: 'This is the counsel of Ilúvatar in my heart: that we should take up again the mastery of Arda, at whatsoever cost, and deliver the Quendi [Elves] from the shadow of Melkor.' Then Tulkas was glad; but Aulë was grieved, foreboding the hurts of the world that must come of that strife. But the Valar made ready and came forth from Aman in strength of war, resolving to assault the fortresses of Melkor and make an end. Never did Melkor forget that this war was made for the sake of the Elves, and that they were the cause of his downfall. Yet they had no part in those deeds, and they know little of the riding of the might of the West against the North in the beginning of their days.
Melkor met the onset of the Valar in the North-west of Middle-earth, and all that region was much broken. But the first victory of the hosts of the West was swift, and the servants of Melkor fled before them to Utumno. Then the Valar passed over Middle-earth, and they set a guard over Cuiviúnen; and thereafter the Quendi [Elves] knew nothing of the great Battle of the Powers, save that the Earth shook and groaned beneath them, and the waters were moved, and in the north there were lights as of mighty fires.
But at the last the gates of Utumno were broken and the halls unroofed, and Melkor took refuge in the uttermost pit. Then Tulkas stood forth as champion of the Valar and wrestled with him, and cast him upon his face; and he was bound with the chain Angainor that Aulë had wrought, and led captive; and the world had peace for a long age.
This is by no means the utter end. Melko commits further destruction through deception and treachery, winning the upper hand from time to time, then losing it. The verdict must be:
Team versus Team: Tie.
It will take another faction to tip the scales. One does.