The Inherent Incompatability of Morgoth and Sauron

[Zigûr]

Originally Posted by Nikkolas

Did he never know the true mind of his master? That if the forces of evil had prevailed and the Host of the West not come, Melkor probably would have done nothing but perhaps start reducing his grand empire to rubble?

I find this observation from 'Notes on motives in the Silmarillion' in the "Myths Transformed" section of Morgoth's Ring to be quite relevant regarding Sauron's attitude, especially after the Downfall of Númenor:

"He probably deluded himself with the notion that the Valar (including Melkor) having failed, Eru had simply abandoned Eä, or at any rate Arda, and would not concern himself with it any more."

Note that this is specified as a delusion, which is the best way of explaining how Sauron, who had irrefutable knowledge of the truth and power of his Creator, could still have the motivations that he did.
More importantly, however, is that phrase "the Valar (including Melkor) having failed."
So Sauron considered Melkor to be a failure, seemingly along with or in the same way as his enemies, the Valar. In what way?

1) Melkor had failed by being defeated and expelled from Eä (or at least Arda). This seems unlikely if we're to read that phrase as Sauron perceiving Melkor and the faithful Valar as equivalent failures.
2) Melkor had proven himself to be too weak, flawed of character or lacking in conviction to carry out his plans, not unlike (it could be argued) the Valar themselves, who had seemingly become very passive.

We can't forget how Morgoth develops as a character. In the beginning Sauron must have perceived Melkor as a being not unlike himself, thinking that Melkor's desire for lordship was equivalent to his own love of order, or at least thinking that the two aims were highly compatible. It was only as he spent more and more of his power in fixation on terrestrial domination that Melkor became the nihilistic Morgoth, evil but also crippled, desiring now only destruction in his resentment of his Creator and his kin.
I think this explains the situation: Sauron did not perceive his incompatibility with Morgoth because at first there was no incompatibility; it developed over time as Morgoth's intentions decomposed. But apparently Sauron did, in the end, come to see Morgoth as a failure, and I would argue that it makes decent sense to imagine that this was because he perceived Morgoth as having failed to uphold the only cause he thought was worthwhile in Arda: the establishment and maintenance of order. I think that in his mind there would be no difference between Morgoth's nihilism and the Valar's passivity. For a being who seemingly believed that the ends entirely justified the means, the situation must have seemed completely rational.