The international trailer has debuted for The Amazing Spider-Man 2, and it not only contains some different footage, it also has a much more optimistic tone than the first American trailer.

"You know what it is I love about being Spider-Man?  Everything!"  Peter (Andrew Garfield) says over the exact same opening footage as in the American trailer where he was lamenting his lot in life (see "First 'Spidey 2' Trailer").
The clip features a laugh while hiding from Aunt May (Sally Field) and some glimpse of Peter’s relationship with Gwen (Emma Stone), as well as a few different shots of battles with Rhino and Electro.  No teasers about Venom or the Sinister Six though (see "Venom, Sinister Six Movies").
The Amazing Spider-Man 2 opens in theaters May 2, 2014.