If we are going to make a comparison between to evil (negative) powers, it make sense, I believe, to understand their opposition to the power of Eru which was the source of their own existence.
It seems, Melkor was given powers to operate with any kind of substance and was able to shape it into virtually anything (his only predicament was light, which is not a substance - Melkor could shut it out or steal it but could not call it into being out of nothing). A bigger gap between Melkor and Eru lies in their relationship to time. Melkor, with all his powers, was a temporal (albeit an immortal) creature who apprehends the past, the present and the future roughy in a way we do. He lives in Time. For Eru, on the contrary, all moments of time are "present" simultaneously. Time exists within Eru's mind. I would roughly liken Eru to an author of a story, in which all others serve just as characters. While Hamlet was facing his challenges and choices (to be or not to be...), Shakespeare already knew how it was going to end...
The destiny of Ea was presented to Ainur as the Music, which they were able to enrich, developing the theme given by Eru; Melkor even succeeded to bring in a theme of his own, which contradicted the main one, and subsequently, caused a discord. It all finished, however, on Eru's terms: Melkor's theme was harmonised with the rest of the Music. Then Ainur were offered a chance to see the music they created embodied in a Universe (Ea) and even participate in its creation, development and demise (and what is music if not a well-temered time?
).
Now we have a string of questions:
How did Ainur, Melkor and Sauron in particular, understand the meaning of the Music?
What kind of idea of Eru did they possess?
What I mean is: did Melkor seriously think he was able to amend the providence, i. e. to re-write the future (the future, that was as present for Eru as all other moments in Time)? Or did he come to a conclusion that his theme was the destiny of Ea, that the latter should be shaped accordingly, that the final harmony means only that voices of other Ainur should yield to his tunes?
What I think is that if he ever had an intention to destroy Arda completely, he had not gained it until the very late stage of his fight. It seems, he wanted to re-shape Arda according to his plan (we don't know what it was) and struggled to remove all obstacles (including Ea's existing constitution if necessary).
I wonder what Sauron could think about the Music. I don't believe he could ever forget it as it must have made the most profound impression on his soul ever. Thus, Melkor needed to work hard to persuade Sauron that his (Melkor's) plan can bore a fruit. It is also very difficult to accept that Sauron could believe that Eru literarily abandoned Ea: Eru's nature doesn't simply allow him to abandon anything that does exist. Either Sauron had a very faulty idea of Eru or he believed that taking responsibility for Middle Earth is The Way - something that Eru would approve or at list tolerate. At least during his brief repentance, if it was a sincere move.
Finally, the situation seduces me to make one more comparison. If Tolkien is "Eru" of his universe, we, readers, resemble children of Eru (men), who live a short but bright life (reading The Hobbit or The Lord of The Rings) and then are taken to Eru to listen to his music and learn the truth about Ea that lies beyond our ordinary experience (reading Silmarillon). And I like this thought