I first watched the BvS trailer yesterday and I have to say, I'm excited!
I feel like the trailer established a clear tone that I hope the movie will follow through with. It appears like DC will continue to differentiate itself from Marvel by giving their films a much darker tone. Although that's the problem many people had with Man of Steel, I feel like it gave the movie an added sense of weight and importance that the Reeve/Donner films lacked (Although they still are slightly better).
Another thing I like about the trailer is how it established Batman as an existing character and made it clear that this movie is not going to be another origin story.
Overall, it seems like Batman will be extremely ticked off at Superman and feels like someone needs to take him down a notch.
Another thing the clip showed us was that the much of the world had very negative views regarding Superman, most notably from the "FALSE GOD" statue and Lex Luthor's awesome line:
"We now know better now don't we? Devils don't come from the Hell beneath us, they come from the sky."
The only thing I didn't like about was the overlapping sound bites. They just seemed kind of confusing to me.
Overall though, I think it was awesome!