Jude law is cool too, but some of the songs on that record sound alittle too pop-punkish for me. There new cd sounds more alternative, like the smiths. I love it. 
I wouldn't classify anything Brand New has done as "alternative". I DEF wouldn't classify the Smiths as alternative. The Smiths is pure british pop-rock. Alternative is weird or very unclassifiable rock. Like the flaming lips. Or polyphonic spree. Or like grunge was when it first hit.
No, if you want to differentiate Deja then say Deja is more Emo-rock. I do agree there is more pop-punk to FW but keep in mind that even the FW ran dual vocals and dual guitars and had a lot of tempo changes. Not to mention how many of the songs are about failure, or being dumped, or just being unhappy. Which is still very emo.
Think of it this way, emo is like having The Ramones sing a bunch of Cure songs.
