Okay, I know this is an old thread but I didn't want to start a new one. I prefer to recycle because it keeps the place cleaner. And it gives a chance to see new opinions now that more films came out!
A few people have mentioned that Vader seemed to be in control, and that he had respect for the Moff. Both could be very true and both would make sense.
However, another to add (not take away or replace the two above suggestions)... Darth Sidious might have been applying the same style of training to his Apprentice (Vader) as what he recieved from his own Master (Darth Plagueis).
"Tell me what you regard as your greatest strength, so I will know how best to undermine you; tell me of your greatest fear, so I will know which I must force you to face; tell me what you cherish most, so I will know what to take from you; and tell me what you crave, so that I might deny you."
By denying Vader the ultimate authority after himself, Sidious was keeping his anger and frustration alive. Just as Plagiueis kept things from Sidious to keep his anger alive, thus making him a better and far more powerful Darth Lord.
We can only assume, Vader was ready to be the true second in command in the years that came after the date 0BBY when the Death Star was destroyed. But it would make sense for a Master to pass on the techniques that he/she had also been taught in their Apprenticeship.
🙂